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The movement of a body subjected to a drag force proportional to the square of the velocity is of great importance in the field of mechanical engineering, since it is a realistic model in the regime of high velocity of the flow. In this paper, the trajectory of a projectile in quasi-vertical launch with quadratic drag is analyzed using the technique of matched asymptotic expansions. Through the asymptotic analysis, approximate analytical expressions for the projectile movement are found. The asymptotic solutions are compared with exact numerical results. [ABSTRACT FROM AUTHOR]

The challenge of creating reliable technology-based resources for science learning is a perennial challenge in Philippine education, with limited learning materials accessible to all learners. This study is about the development of a videocast embedded with physics education technology (PhET) simulation that served as supplementary learning material for grade 9 science in response to the scarcity of dependable visualization materials. The study employed the developmental research design with analysisdesign-development-implementation-evaluation (ADDIE) model as the developmental framework. The vodcast evaluation tool, achievement test questionnaire, and vodcast perception survey questionnaire for students and teachers were used in the data collection, while the Kendall's W statistic, mean, percentage, and gain score were used in the data interpretation. The teacher respondents (N=64) have moderate agreement on the ranking of topic difficulty, with Kendall's W of 0.45. The researcher-made vodcast attained an overall rating of 4.78 from experts, which implies that the vodcast can be very good material for classroom implementation. The developed achievement test has acceptable difficulty and discrimination indices. The implementation stage yielded a low normalized gain, which can be accounted for by unfocused attention during the pandemic. Nevertheless, the voicecasts were found very useful in learning projectile motion, as perceived by both students and teacher-observers. [ABSTRACT FROM AUTHOR]

This paper proposed an efficient research method for high-dimensional uncertainty quantification of projectile motion in the barrel of a truck-mounted howitzer. Firstly, the dynamic model of projectile motion is established considering the flexible deformation of the barrel and the interaction between the projectile and the barrel. Subsequently, the accuracy of the dynamic model is verified based on the external ballistic projectile attitude test platform. Furthermore, the probability density evolution method (PDEM) is developed to high-dimensional uncertainty quantification of projectile motion. The engineering example highlights the results of the proposed method are consistent with the results obtained by the Monte Carlo Simulation (MCS). Finally, the influence of parameter uncertainty on the projectile disturbance at muzzle under different working conditions is analyzed. The results show that the disturbance of the pitch angular, pitch angular velocity and pitch angular of velocity decreases with the increase of launching angle, and the random parameter ranges of both the projectile and coupling model have similar influence on the disturbance of projectile angular motion at muzzle.

Copyright of Latin-American Journal of Physics Education is the property of Latin-American Physics Education Network and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

The motion of any material body after be launched from some point in Earth surface start to follow a trajectory determined by two different interactions, the gravitational attraction and the resistance to his movement caused by the contact with the molecules of the medium in which it travels. Considering that a huge amount of physics problems remains not even mentioned on physics courses due to the requirements of strong mathematical background or computational effort. The authors propose a new and easier approach to introduce the study of complex problems in introductory physics courses, based on neural networks and machine learning. Through one simple example of classical mechanics with artificial intelligence the authors are supposed to contribute with the introduction of new technologies to physics learning.

This research aims to evaluate how physics education students respond to the use of tracker software in the implementation of physics laboratory experiments covering projectile motion. The study was conducted in the physics laboratory at the Universitas Kristen Indonesia Toraja (UKI Toraja) and involved 10 (ten) physics education students. Research data were obtained through questionnaires and analyzed quantitatively by calculating percentages. The utilization of tracker software in the implementation of projectile motion experiments enables students to easily observe and analyze the phenomenon of projectile motion. Students feel that experiments on projectile motion using tracker software are relatively straightforward to understand and learn. The results of student responses to the implementation of physics laboratory experiments involving tracker software in projectile motion show an approval rate of 64.4%. Therefore, it can be concluded that students exhibit a positive response and agree with the use of tracker software in physics laboratory experiments. [ABSTRACT FROM AUTHOR]

Rockfalls have a tremendous effect on development plans in mountainous regions. Both civil structures and lives are at risk from rockfalls. Frequent failure, rather than the size of a rockfall, is the key factor in including rockfalls to the class of common natural hazards in hilly areas. The Western Ghats region of India is vulnerable to rockfall due to its geology and geography. Kinematic analysis has suggested the possible failure pattern of the slopes by considering structural mapped data. Planar failure, as well as toppling failure, are the possibility for structurally controlled slopes for the region. Identification of the most appropriate model and defining the failure mechanism is one of the most challenging steps in protection planning for rockfalls. To develop a precise real-field model, the Python-Simulated Rockfall Model (PSRM) is demonstrated for consideration of all the parameters, including the advantages of assigning different sizes and shapes of boulders. The proposed model and the existing RocFall software have been comprehensively compared to validate the results. The bounce height, run-out distance and the falling velocity obtained from the PSRM are more realistic according to the real-field scenario. The PSRM can provide various output data, which are necessary for disaster-management planning for rockfalls. Unlike the RocFall simulation, the PSRM neither overestimated nor underestimated the value. The flexibility of estimating different parameters at each step makes the PSRM more applicable in rockfall analysis. [ABSTRACT FROM AUTHOR]

The projectile motion (PP) in a vacuum is re-examined in this paper, taking into account the relativistic mass in special relativity (SR). In the literature, the mass of the projectile was considered as a constant during motion. However, the mass of a projectile varies with velocity according to Einstein's famous equation m = m 0 1 − v 2 / c 2 , where m 0 is the rest mass of the projectile and c is the speed of light. The governing system consists of two-coupled nonlinear ordinary differential equations (NODEs) with prescribed initial conditions. An analytical approach is suggested to treat the current model. Explicit formulas are determined for the main characteristics of the relativistic projectile (RP) such as time of flight, time of maximum height, range, maximum height, and the trajectory. The relativistic results reduce to the corresponding ones of the non-relativistic projectile (NRP) in Newtonian mechanics, when the initial velocity is not comparable to c. It is revealed that the mass of the RP varies during the motion and an analytic formula for the instantaneous mass in terms of time is derived. Also, it is declared that the angle of maximum range of the RP depends on the launching velocity, i.e., unlike the NRP in which the angle of maximum range is always π / 4 . In addition, this angle lies in a certain interval [ π / 4 , π / 6) for any given initial velocity (

Conventional teaching is rapidly changing, and online and simulated software are adding up in teaching. Simulations on spreadsheets have become popular due to their ubiquitous and easily understandable. In this paper, we demonstrate three physics topics: the motion of a charged particle in a uniform magnetic field, the motion of a projectile, and the simple harmonic motion of a simple pendulum. The third example is a demonstration of an experiment on a simple pendulum to find the time period of a simple pendulum and study the amplitude's effect on it. Students can perform the whole experiment on the spreadsheet in real-time. [ABSTRACT FROM AUTHOR]

This study intended to assess the extent to which computer-simulated teaching tools influence Rwandan senior four students' understanding of graphs of projectile motion. Two schools were purposively selected, and 54 students were grouped in the control and experimental groups. Students' scores on a multiple-choice test were collected and analyzed using frequencies and inferential statistics. Results showed that students in the experimental group got the average normalized gain in the medium range, t(36)=3.944, p<0.01 whereas in the control group it was in the low range, t(16)=1.788, p>0.05. It was found that students in the experimental group improved their understanding of graphs of projectile motion better than students who were taught using traditional methods, t(52)=-2.194, p=0.033. The study shows that using computer-simulated teaching tools influences positively students' understanding of graphs of projectile motion. The use computer-simulated teaching tools in teaching projectile motion is recommended for physics teachers and further studies. [ABSTRACT FROM AUTHOR]

Copyright of Momento: Revista de Física is the property of Universidad Nacional de Colombia, Departamento de Fisica and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

ABSTRAK Penelitian ini bertujuan untuk memperoleh produk Lembar Kerja Peserta Didik (LKPD) berbasis discovery learning berbantuan software Modellus pada pokok bahasan gerak parabola yang valid dan praktis untuk digunakan sebagai media pembelajaran. Penelitian ini dilakukan dengan menggunakan metode Research and Development (R&D) dengan model pengembangan 4D Thiagarajan. Model pengembangan 4D terdiri dari empat tahap utama yaitu tahap define, tahap design, tahap develop, dan tahap disseminate. Namun, dalam penelitian ini peneliti membatasi penggunaan model pengembangan 4D ini hanya sampai pada tahap develop. Instrumen pengumpulan data dilakukan melalui wawancara, angket analisis karakteristik peserta didik terhadap kebutuhan media pembelajaran, angket validasi ahli media dan ahli materi, serta angket respon pendidik dan peserta didik terhadap kepraktisan produk. Hasil penelitian menunjukkan bahwa persentase nilai validitas produk berdasarkan ahli media adalah 93,33% dengan kriteria sangat valid dan ahli materi adalah 97,64% dengan kriteria sangat valid. Persentase nilai kepraktisan produk berdasarkan respon pendidik adalah 94% dengan kriteria sangat praktis dan respon peserta didik adalah 92,10% dengan kriteria sangat praktis. Dengan demikian, Lembar Kerja Peserta Didik (LKPD) berbasis discovery learning berbantuan software Modellus pada pokok bahasan gerak parabola yang dikembangkan telah memenuhi kriteria valid dan praktis untuk digunakan sebagai media pembelajaran fisika. Kata kunci: discovery learning; gerak parabola; lembar kerja peserta didik (lkpd); software modellus ABSTRACT This study aims to obtain a student worksheet product based on discovery learning assisted by Modellus software on this topic of projectile motion that is valid and practical to be us as a learning medium. This research was conduct using the Research and Development (R&D) method with the Thiagarajan 4D development model. The 4D development model consists of four main stages, namely the define stage, the design stage, the developing stage, and the disseminated stage. However, in this study, the researcher limits the use of this 4D development model to only the development stage. Instruments of data collection were carrie out through interviews, questionnaires to analyze the characteristics of students on the needs of learning media, validation questionnaires from media experts and material experts, well questionnaires for teacher and student responses to the practicality of the product. The results showed that the percentage value of product validity based on media experts was 93.33% with very valid criterium and material experts were 97.64% with very valid criterium. The percentage value of the practicality of the product based on the teacher's response is 94% with very practical criterium, and the student response is 92.10% with very practical criterium. Thus, the Student Worksheet based on discovery learning assisted by Modellus software on the subject of projectile motion developed has met the valid and practical criterium to be used as a physics learning medium. Keywords: discovery learning; projectile motion; student worksheet; software modellus

This research studied the effectiveness of the simulation-based learning assisted with scaffolding approach to address students' misconceptions (MCs) about projectile motion. The five MCs were related to the direction of the force acting on an object (MC1), the acceleration of an object at the top of the trajectory (MC2), the directions of velocity and acceleration during projectile motion (MC3), the time of flight of objects (MC4), and the relationship between the range of projectile motion and angle of projection (MC5). This study was a pre-experimental design using both quantitative and qualitative data. The sample comprised 35 tenth-grade Thai high school students who were chosen using the cluster sampling technique. The teaching method consisted of three steps: a briefing, simulation, and debriefing. Each step was assisted with scaffolding to guide and help the students. The MCs tests consisted of five multiple-choice questions with a four-tier diagnostic test, and the tests were used as a pre-test, end-of-class test, and end-of-topic test. Six semi-structured interview questions were used to obtain in-depth data. The results indicated that MC1, MC2, MC3, MC4, and MC5 were addressed by 11.1%, 85.7%, 57.2%, 57.2%, and 61.5%, respectively, at the end-of-topic test. Students who had MCs in the pre-test changed their understanding of the concepts in MC2, MC3, MC4, and MC5 by 57.1%, 14.3%, 28.6%, and 53.8%, respectively. None of the MC students in MC1 understood the concept at the end-of-topic test. Nevertheless, the overall results showed increased students' understanding of all conceptions. [ABSTRACT FROM AUTHOR]

The motion of any material body after be launched from some point in Earth surface start to follow a trajectory determined by two different interactions, the gravitational attraction and the resistance to his movement caused by the contact with the molecules of the medium in which it travels. Considering that a huge amount of physics problems remains not even mentioned on physics courses due to the requirements of strong mathematical background or computational effort. The authors propose a new and easier approach to introduce the study of complex problems in introductory physics courses, based on neural networks and machine learning. Through one simple example of classical mechanics with artificial intelligence the authors are supposed to contribute with the introduction of new technologies to physics learning. [ABSTRACT FROM AUTHOR]

In this work, we developed the equations regarding the movement of a smooth sphere in the presence of drag forces, in the high-speed regime, where the resistive force is proportional to the square of its velocity. This regime is commonly found in various everyday situations in which objects of all kinds are thrown into the air. The equations studied in basic undergraduate courses disregard the drag of the air and, therefore, are idealized equations, not consistent with the actual nature of the observed movement. Here, we intend to assist the reader in traveling a bit closer to reality and contemplating the complexity of some equations when we try to model the world as it truly is. This subject is of extreme importance for undergraduate students in the field of aeronautical engineering and mechanics, as it is essential to understand how drag forces affect the behavior of objects in motion. [ABSTRACT FROM AUTHOR]

Copyright of Latin-American Journal of Physics Education is the property of Latin-American Physics Education Network and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

The projectile motion (PP) in a vacuum is re-examined in this paper, taking into account the relativistic mass in special relativity (SR). In the literature, the mass of the projectile was considered as a constant during motion. However, the mass of a projectile varies with velocity according to Einstein’s famous equation m=m01−v2/c2, where m0 is the rest mass of the projectile and c is the speed of light. The governing system consists of two-coupled nonlinear ordinary differential equations (NODEs) with prescribed initial conditions. An analytical approach is suggested to treat the current model. Explicit formulas are determined for the main characteristics of the relativistic projectile (RP) such as time of flight, time of maximum height, range, maximum height, and the trajectory. The relativistic results reduce to the corresponding ones of the non-relativistic projectile (NRP) in Newtonian mechanics, when the initial velocity is not comparable to c. It is revealed that the mass of the RP varies during the motion and an analytic formula for the instantaneous mass in terms of time is derived. Also, it is declared that the angle of maximum range of the RP depends on the launching velocity, i.e., unlike the NRP in which the angle of maximum range is always π/4. In addition, this angle lies in a certain interval [π/4,π/6) for any given initial velocity (

The aim of this paper was to present reflections on the teaching of physical science using the topic of projectile motion as a launch pad. It focused on the teaching model and what the Department of Basic Education expects from teaching physical science subjects. Furthermore, it looked at some of the challenges regarding teaching physical science in general and in particular to the projectile motion topic. It looked at empirical studies in projectile motion to situate the current research interest to articulate gaps in the topic and the subject. It concludes with recommendations and highlights a need to focus on all grades when teaching physical science subjects, particularly projectile motion than only in grade 12 as stipulated by Curriculum Assessment Policy Statement. The team teaching approach amongst curriculum implementers and subject teachers is also accentuated, and further investigations are proposed. [ABSTRACT FROM AUTHOR]

Copyright of Industrial Minerals & Processing / Huagong Kuangwu yu Jiagong is the property of Industrial Minerals & Processing Editorial Office and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Linear vibratory feeder is one of the most extensively used part feeding systems in a production line. The part motion on the feeder can be sliding or hopping or a combination of these two. Based on the dynamics of part motion this paper identifies three distinct regimes. A mathematical model was developed that can predict the trend in conveying velocity in these regimes. This model can provide the parts position as a function of time and has considered relative displacement between the part and the conveying surface. The simulation was validated by performing experiments for a range of vibration frequencies and amplitudes. [ABSTRACT FROM AUTHOR]

The analysis of wind-influenced projectile motion in the case of linear and nonlinear (quadratic or nonquadratic) drag force is reviewed. For quadratic or more general nonlinear drag force, the results can be obtained only numerically, because the governing coupled differential equations of motion do not allow an analytical solution, although there is a closed-form relationship between the velocity and an appropriately defined angle parameter in the case of quadratic drag. For linear drag force, the entire solution, including the expressions for the time-variation of velocity components and the shape of the trajectory, can be derived in closed form. Forward-to-backward transition of the direction of motion of a projectile launched against horizontal wind is analyzed. If during different phases of motion different types of drag apply, the extents of these phases are not known in advance and the general expression for the drag force that encompasses the entire range of the Reynolds number must be used throughout the motion, in conjunction with the numerical solution of the governing differential equations. The transition from nonquadratic to quadratic drag is discussed. Illustrative examples of wind-influenced projectile motion considered in this review include the motion of golf balls, respiratory droplets, powder particles, and flea beetles. [ABSTRACT FROM AUTHOR]

Analysis of crime scenes involving single-fire-gun projectiles requires the determination of the direction of arrival of a projectile at the target and other factors to reconstruct events. The movement of a projectile can be analyzed by applying Euler’s equations to a solid symmetrical rigid body. The present work starts from a Newtonian reformulation of these equations to show that, in the presence of a gravitational field, the system can be expressed with a complex variable nonlinear equation, where the inclusion of small nutation variables allows us to find possible solutions. As a particular case, we analyzed the movement of a 9-mm projectile fired from distances greater than 1 m to demonstrate that the direction of arrival of the projectile at the target cannot be traced by a stick placed in the target hole, as is usually performed in crime investigations. A series of shots were fired from distances varying between 1 m and 7 m. Impact data were recorded on Riemann planes of projection for the description of nutation and precession motions, allowing the observation of the motion dynamics of the projectile. We show that the direction of arrival at the target can be determined approximately from the analysis of the nutation and precession curves through Riemann planes of projection. The results presented in this work will allow more accurate judgements to be made in judicial investigations.

IDENTIFICATION OF MISCONCEPTION AND COGNITIVE CONFLICT OF PHYSICS: A CASE RELATED TO CONCEPTUAL CHANGE Abstract Misconceptions still often occur when learning physics. This study aims to identify students' misconceptions and their relationship with cognitive conflict in terms of conceptual change. This research used mixed methods explanatory design methods. The subjects in this study were three students from SahabatQu High School, Yogyakarta. The students studied were categorized into three, namely low, medium, and high ability students. Information related to student abilities is obtained from physics teachers and student learning test results. A conceptual change interview guide, conceptual change observation sheet, cognitive conflict questionnaire, and parabolic motion material misconceptions tests were used as supporting instruments to obtain the desired results in research. The learning process uses a PhET simulation. The results showed that high, medium and low ability students still had misconceptions when learning parabolic motion material. Cognitive conflict in high, medium and low ability students is included in the low and moderate categories with a percentage of 8.33% - 41.67%. All students have not been able to experience the four thought processes so that there are still misconceptions on some topics such as the highest point and the farthest distance based on the projectile motion's elevation angle. Abstrak Miskonsepsi masih sering terjadi pada saat pembelajaran fisika. Tujuan penelitian ini adalah mengidentifikasi miskonsepsi siswa dan hubungannya dengan konflik kognitif ditinjau dari perubahan konseptual. Penelitian ini menggunakan metode mixed methods explanatory design. Subjek pada penelitian ini adalah 3 siswa yang berasal dari SMA Sahabatqu, Yogyakarta. Siswa yang diteliti dikategorikan menjadi 3 yaitu siswa berkemampuan rendah, sedang, dan tinggi. Informasi terkait kemampuan siswa diperoleh dari guru fisika dan hasil tes belajar siswa. Pedoman wawancara perubahan konseptual, lembar observasi perubahan konseptual, angket konflik kognitif, dan tes miskonsepsi materi gerak parabola dijadikan instrumen pendukung untuk mendapatkan hasil yang diinginkan dalam penelitian. Proses pembelajaran menggunakan simulasi PhET. Hasil penelitian menunjukkan bahwa siswa berkemampuan tinggi, sedang, dan rendah masih memiliki miskonsepsi pada saat pembelajaran materi gerak parabola. Konflik kognitif pada siswa berkemampuan sedang dan rendah termasuk dalam kategori rendah dan siswa berkemampuan tinggi termasuk dalam kategori sedang. Seluruh siswa belum mampu mengalami empat proses berpikir sehingga masih menyisakan miskonsepsi pada beberapa submateri seperti titik tertinggi dan jarak terjauh berdasarkan sudut elevasi gerak parabola.

The main problem of this study is that students who are not able to gain the minimum score were not given remedial teaching and learning that were adjusted to their learning style. This study aimed to determine the effect, improvement, and effectiveness of the use of projectile motion props in remedial teaching on kinesthetic style students learning outcomes and students’ response to the use of the props. The research method used in this study was a quasi-experiment with nonequivalent control group design. Hypothesis test results of the post-test results with the Mann-Whitney U test at the confidence level of 95% (α = 0.05) obtained the significance value (2-tailed) that was 0.000. Alternative research hypotheses (H1) were accepted (there were effects of projectile motion props on remedial teaching on kinesthetic style student learning outcomes). The kinesthetic style student in the experimental group successfully gained 0.64 (middle category) in their learning outcomes, and the controlled group students gained less only 0.31 (middle category) in their learning outcomes. In the cognitive domain of C2 (understanding), the experimental group students experienced the highest increase, which was 0.72, while the controlled group gained only 0.50. The effectiveness of remedial teaching in the experimental group was very effective (80%); meanwhile, in the controlled group, it showed ineffectiveness (28%). Students of kinesthetic style’s response are very good (81%) on the use of projectile motion props.

In this manuscript the fractional form of wind-influenced projectile motion equations which have a significant place in physics is extensively investigated by preserving dimensionality of the physical quantities for fractional operators and features of wind-influenced projectile motion are computed analytically in view of Atangana-Baleanu (ABC) fractional derivative in Caputo sense. Moreover, ABC fractional derivative with (n + α)th-order and its Laplace transform (LT) are obtained, α ∈ [0, 1] and n ∈ N. A comparative analysis based on the classical case is carried out in order to shed more light on the potent of the ABC fractional operator. Hence we present the results for some values of α, k friction constant, different wind effects and different masses in 3D illustrations by comparing Caputo fractional operator. Thus, we can observe trajectory, time of flight, maximum height and range clearly. Moreover, the obtained results are shown to correspond to the classical case while the order α → 1.

A Science, Technology, Engineering and Mathematics (STEM) tool is proposed in this manuscript; which consists of an interactive, simple and low-cost computer based simulation and game, with the aim of easing the teaching/learning process regarding the physics concept of projectile motion. The novelty of this proposal relies on the use of a joystick shield used as the input device that changes the projectile shooting angle, the initial velocity and height in a simulation coded in S4A (Scratch for Arduino). The electronic interface is based on an Arduino UNO and a dual-axis joystick module. This educational resource is suitable to be implemented in graduate or undergraduate physics laboratories, classrooms or even at home. [ABSTRACT FROM AUTHOR]

Inconsistent filtering of force plate data persists in published studies. Previous evidence suggests that low pass filtering produces the largest error when calculating jump height, but used jump height from unfiltered force plate data as the criterion. This study investigated the effects of low pass filtering on jump height calculated from force plate data, using jump height recorded from optical motion capture as the criterion. Unfiltered as well as both single and dual pass filtered data, with cutoff frequencies of 100, 50 and 5 Hz, were used to calculate jump height using take-off velocity (TOV) and take-off velocity summed with displacement (TOV+s). The TOV+s method using the 5 Hz single pass filtered signal, best agreed with the criterion (p <.001). This was accomplished through changes in the force-time signal that decreased velocity and increased displacement at take-off (p <.001). This is contrary to previous recommendations and informs the development of standard procedures. [ABSTRACT FROM AUTHOR]

Research in the past decades has repeatedly revealed that first year university students struggle to understand two-dimensional projectile motion concepts. In contrast to high school, projectile motion frequently makes use of components and it requires at least a basic understanding of trigonometry concepts. To follow the lessons and generate conceptual understanding in two-dimensional projectile motion, students need to connect the concepts developed in the last three years of high school. The present study compared the effects of two instructional approaches, i.e. projectile motion Physics Education Technology (PhET) simulation vs. phenomenon-based experiential learning, on students' conceptual understanding of the integration of motion along two independent axes among first-year physics students. A purposive sample consisted of 154 first-year physics students at a public university in South Africa. The study adopted an experimental, mixed-method research design. A self-developed and piloted Projectile Motion Conceptual Test and semi-structured interviews with 12 students from across the performance spectrum were used for data collection. A reliability coefficient of 0.72 was established using the Kuderson–Richardson correlation moment coefficient. The results denoted that PhET simulation outperformed phenomenon-based experiential learning in improving students' conceptual understanding of the integration of motion along independent axes in projectile motion. The ANOVA-test showed that the PhET groups achieved significantly higher scores on the post-test than phenomenon-based experiential learning groups. The findings of this study are diagnostic and they assist module designers in determining conceptual difficulties students face in projectile motion. [ABSTRACT FROM AUTHOR]

Analysis of crime scenes involving single-fire-gun projectiles requires the determination of the direction of arrival of a projectile at the target and other factors to reconstruct events. The movement of a projectile can be analyzed by applying Euler's equations to a solid symmetrical rigid body. The present work starts from a Newtonian reformulation of these equations to show that, in the presence of a gravitational field, the system can be expressed with a complex variable nonlinear equation, where the inclusion of small nutation variables allows us to find possible solutions. As a particular case, we analyzed the movement of a 9-mm projectile fired from distances greater than 1 m to demonstrate that the direction of arrival of the projectile at the target cannot be traced by a stick placed in the target hole, as is usually performed in crime investigations. A series of shots were fired from distances varying between 1 m and 7 m. Impact data were recorded on Riemann planes of projection for the description of nutation and precession motions, allowing the observation of the motion dynamics of the projectile. We show that the direction of arrival at the target can be determined approximately from the analysis of the nutation and precession curves through Riemann planes of projection. The results presented in this work will allow more accurate judgements to be made in judicial investigations. [ABSTRACT FROM AUTHOR]

Copyright of Ordnance Industry Automation is the property of Editorial Board for Ordnance Industry Automation and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

This paper presents new solutions for twodimensional projectile motion in a free and resistive medium, obtained within the newly established conformable derivative. For free motion, we obtain analytical solutions and show that the trajectory, height, flight time, optimal angle, and maximum range depend on the order of the conformable derivative, 0 < γ ≤ 1. Likewise, we analyse and simulate the projectile motion in a resistive medium by assuming several scenarios. The obtained trajectories never exceed the ordinary ones, given by γ = 1, unlike results reported in other studies.

Two different types of motion were analysed based on video footage using the free software tool named Tracker. One of them involved dropping the football vertically without any spin, the other type was the projectile motion resulted from a goalie punt. The analysis consisted of fitting the time dependence of the coordinates using a sixth order polynomial, then using these functions and other parameters to obtain the drag coefficient as a function of speed and Reynolds number. Similarly to previous works, the drag coefficient showed large differences for the different speeds. The irregularities and asymmetry of the ball also caused the results to be different for the different trials depending on the orientation of the ball, as well as the slight horizontal spin of the ball during its projectile motion. This method can prove to be a useful tool for further studies in a more controlled environment with higher quality new balls. [ABSTRACT FROM AUTHOR]

Projectile motion is studied using fractional calculus. Specifically, a newly defined fractional derivative (the Leibniz L-derivative) and its successor (Λ-fractional derivative) are used to describe the motion of the projectile. Experimental data were analyzed in this study, and conclusions were made. The results of well-established fractional derivatives were also compared with those of L-derivative and Λ-fractional derivative, showing the many advantages of these new derivatives.

Using the Lambert W function, the quadratic resisted projectile motion with an approximation of low-angle trajectory has been studied where the launching point is assumed to be higher than the landing point. Analytical solutions for the range and the time of flight are presented in terms of the secondary branch of the Lambert function W−1.

This paper proposes a new stochastic metaheuristic optimization algorithm which is based on kinematics of projectile motion and called projectile-target search (PTS) algorithm. The PTS algorithm employs the envelope of projectile trajectory to find the target in the search space. It has 2 types of control parameters. The first type is set to give the possibility of the algorithm to accelerate convergence process, while the other type is set to enhance the possibility to generate new better projectiles for searching process. However, both are responsible to find better fitness values in the search space. In order to perform its capability to deal with global optimum problems, the PTS algorithm is evaluated on six well-known benchmarks and their shifted functions with 100 dimensions. Optimization results have demonstrated that the PTS algoritm offers very good performances and it is very competitive compared to other metaheuristic algorithms. [ABSTRACT FROM AUTHOR]

This paper addresses the modeling of projectile motion using fractional models vis-a-vis experimental data. Recently, it was shown that an auxiliary parameter (σ ) needs to be included in the fractional modeling to preserve the dimensionality of the physical quantities. In previous studies, σ was subjected to several restrictions without considering clear and meaningful reasons. Such problems are overcome here and a method for estimating σ using the experimental data is introduced. A new solution for the two-dimensional projectile motion using the Caputo's fractional derivative is obtained. An explicit formula for the trajectory of the projectile in vacuum is first derived. Then, the projectile parametric equations in a resistant medium are expressed in terms of the Mittag–Leffler function. The transcendental equations for the time of flight and the time of maximum height are solved numerically. The model agrees with the classical one as the fractional order tends to 1. In view of the superior results, the current numerical modeling approach is validated for this real-world application. [ABSTRACT FROM AUTHOR]