摘要或動機

上體育課的時候看到同學投空心球（籃球在沒有碰著籃框的情況下進入籃中），覺得好厲害。因此，我們利用相關的數學知識與運動原理來討論籃球投出後的運行軌跡，以及影響其命中率的相關因素。我們得知籃球的運行軌跡是一條拋物線，並求出其二次方程式；並利用標準籃球直徑與籃框直徑找出籃球進入籃框的最小入射角。若要提高命中率，必須考慮籃球投出時的投射角、初速度、籃球投出時的高度以及籃球與籃框水平距離之間的相關影響。此外，我們藉由電腦軟體列出相關數據提供作為實際投籃時的參考，並藉此進一步分析上述因素如何影響籃球運行軌跡以及如何提高投籃的命中率。Those who always shoot nothing but the net in basketball games were always heroes to me. I have being thinking for a long time how to become a person of that kind. For this, we investigated the trajectory of shooting a basketball and the factors to increasing the field goal percentages through our knowledge on mathematics and physics. We have obtained that the trajectory is in fact a parabola and, we further, found its quadratic equation. We also derived the minimal incident angle from the diameters of the standard basketball and hoop as well as the quadratic equation we have found. To raise the field goal percentages, some important factors must be taken into consideration, such as the vertical and horizontal distance between the basketball and the hoop, the incident angle and the initial velocity of shooting. Finally, we provide some concerning data for reference, and analyzed how the important factors we have mentioned above have affected our basketball trajectory and how, of the most importance, to increase the field goal percentages