projectile motion
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Tumble dryers are widely used for drying garments, but felting shrinkage can be caused to wool garments during the tumble drying process. To dry wool fabrics or garments in tumble dryers, the flat dry function has been introduced in the dryers; however, the energy efficiency is very low. The current study investigated fabric movement at different rotation speeds in the tumble dryer and their resultant performances in terms of specific moisture extraction rate, evenness of drying, fabric shrinkage, and fabric smoothness. For shrink-resist-treated wool fabrics, tumble drying at the rotation speed to keep fabric movement in projectile motion accompanied with occasional tumbling could achieve better energy efficiency, drying uniformity, and fabric smoothness. For untreated wool fabrics, introducing vertical movement to the flat dry in the tumble dryer can improve the heat exchange between the fabric and hot air, resulting in an increase in energy efficiency of approximately 30% compared with motionless flat drying. Wool fabric shrinkage can be controlled at less than 2% with the smooth appearance of fabric at grade 3.5 after drying under the recommended drying condition. This study could help tumble dryer manufacturers design optimal drying methods for wool fabrics with the potential for the reduction of energy consumption.

Abstract A convenient approximated analytic solution is proposed for the problem of the motion of a body under a resistive force, acting in the magnitude of the squared velocity of the body. This solution is an explicit function of time, that keeps a good behavior both near the initial state and far from the initial state. To obtain a general analytic solution, we firstly used a reduction principle to be able to manipulate scalar objects, and we analyzed limit behaviors, both near the initial state and far from the initial state. Secondly, we proposed an approximated analytic solution with heuristics based on the built knowledge. Finally, a robust and stable integration scheme is proposed, based on the obtained analytic solution. We compared the scheme with other standard integration schemes.

The influence of the force of the quadratic resistance of the medium on the change in some interesting characteristics of the motion of the projectile, which take place when the projectile moves in vacuum, is investigated. Loci are constructed numerically (and partly analytically) that ensures maximization of the arc length of the projectile trajectory and a non-decreasing of the length of the radius-vector. As examples, the motion of a baseball, a tennis ball and a badminton shuttlecock is studied.

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.

Abstract This research aimed to describe undergraduate students’ misconception about projectile motion after learning physics during the Covid-19 pandemic era. This research was qualitative research with a descriptive method. The subjects were 52 first-year undergraduate students who took physics courses. Data collecting methods used in this research were a test, questionnaires, and interviews. The test was taken from Physics by Giancoli with an additional question about certainty of response index (CRI). Data from the test were analyzed by categorizing it into lack of knowledge, knowledge of correct concepts, and misconception while open-ended questionnaires and interviews were used to help to clarify the condition. The test results indicated that 5.13% of students in lack knowledge, 28.85% the knowledge of correct concepts, and 66.02% in misconception. The questionnaire responses showed that students learned physics via online meeting with direct instruction model and ask-answer method, exercised with only applied problem (C3), and virtual practicum. The interviews showed that only a few of the students learned physics and responded to the lecturer during the online meeting. The results are that the majority of first-year undergraduate students are in misconception after learning physics during the Covid-19 pandemic era and need remedial learning about projectile motion.

Abstract Basketball is a sport, played worldwide by people of all ages, from young to old. The most important skill that a football player should have is shooting. Shooting the ball into the hoop involves projectile motion. The ability of a player to shoot will determine the scores of his/her team. The angle and initial velocity taken during the shooting, plays a vital role, so that a perfect shooting could be achieved. This work has been conducted to determine the optimal throwing angle and initial velocity that a player should take in order to get the best shooting. The relationship of these factors were investigated: the throwing angle and player’s height, initial velocity with the player’s height, as well as the throwing angles versus time taken for the ball to reach the hoop. Our focus is to maximize the height of the ball, before it is thrown. Newton’s law and the concept of projectile motion were applied using a calculus-based model. Relationship between the player’s height with the initial velocity, optimal throwing angle and time taken for the ball to reach the hoop were discussed. Perfect optimal release angle were determined for thirty data of NBA players. It shows that the player’s height is inversely proportional to the initial velocity and the optimal throwing angle. The obtained results also concluded that the optimal throwing angle is directly proportional to the time taken for a ball to reach its maximum height.

When undergraduate students just got into the physics field, it might be difficult for them to understand, think, and imagine what is happening in certain phenomenons [6]. For example, when two objects have different masses and velocity collide into each other, how are they going to act? Are they going to stop, bounce away from each other, or stick together? This simulation helps the students who do not feel comfortable imagining these scenarios. Currently we only have the gravitation lab, the trajectory lab, and the collision lab. The gravitation lab is a planet orbiting a sun, where the users can input different masses for the sun and planet, and the radius (in AU), the program will then calculate the gravitational force and orbital period while the planet starts orbiting its sun at a certain speed [7]. The trajectory lab is an object doing projectile motion, where the user input variables like initial velocity, angle, height, and acceleration, the program will present current position and velocity on the screen as the object doing projectile motion [8]. The collision lab is where the user input the masses and velocities for the two objects, and after the user decide the collision is going to elastic or not, set the lab and press start, the program will calculate the total momentum and kinetic energy and have it on the right side of the screen while the objects starts colliding [9].

This paper presents a new fresh theoretical study of the ballistic penetration phenomena into hard materials due to low-energy bodies' motion. This model based on the energy balance between the kinetic energy of the piercing body and the protective body thermal energy. Following this equilibrium alongside the equation of the projectile motion, the resulting deceleration value is analytically calculated. Substituting the obtained deceleration value into the kinematic equilibrium results with the penetration thickness expression as well as the time of penetration inside the mono and multi layers materials (like, monolithic and composite materials). In addition, equivalently to the Johnson-Cook model, a proposed impact stress for penetrative and non-penetrative cases was developed. Additionally, a residual velocity expression alongside the evaluation of the total energy and deceleration parameters were also determined. Key parameters are the projectile effective length, which defines the projectile geometry alongside the material strength parameters (heat capacity, Yield, compressive and tensile strengths). Finally, good numerical agreement (order of magnitude and numerical values) has been found between various literature experimental tests and current analytic solution for the kinematic parameters.