# 分析學生如何利用二維拋體軌跡圖解題

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2015

## Abstract

This work is focused on student learning of two-dimension projectile motion. A data graph with five trajectories mimics the trace of 5 projectiles by varying the initial launch angle, vertical height and horizontal range. However, the vertical scale of the data graph is in unit of 100 m, while the horizontal scale is in unit of 1000 m. The freshman of Department of Mathematics, Physics, Chemistry, Life-science, Earth Sciences, and Industrial Education of National Taiwan Normal University participated the 30-minitue test on their very first class of General Physics Laboratory. A total of 257 freshmen took the exam. Seventy-seven sophomores of Department of Physics were also taken the same exam to serve as a reference for comparison. The main purpose of this study is to examine how students solve problems using the information given in a plot diagram of projectile motion. There are two parts of the test question. The first part is to write down the flight-time ordering of the 5 projectiles, and the second part is to find the magnitude ordering of initial speeds. Roughly, around 84% students got the correct answer for the first part, while 15% students for the second part. It is not necessary to compute the flight time nor the initial speed to get the correct answer, however, we do find the higher correct rate for student using formula for the second part. These results were cross-compared with the results of International Physics Olympiad on 9th of November, 2014. 2435 students participated in the exam, and the correct rate of the first part was 90%, that of the second part was 33%. We find that over 50% students do not know the effect of initial launch angle on the initial speed when two trajectories have the same horizontal range, though most of them know that the horizontal range is maximum for a launch angle of 45°for the same initial speeds. Students were trained to know the initial launch angle of 45° gives a maximum horizontal range, they do not know the projectiles having the same horizontal range is the 45 one possess a minimum initial speed.