Problem 317
Firecracker
A firecracker explodes at a height of 100 m above level ground. It breaks into a large number of very small fragments, which move in every direction; all of them have the same initial velocity of 20 m/s.
We assume that the fragments move without air resistance, in a uniform gravitational field with g=9.81 m/s2.
Find the volume (in m3) of the region through which the fragments move before reaching the ground. Give your answer rounded to four decimal places.
爆竹
一枚爆竹在距离水平地面100米的高度爆炸。它分裂成了许多非常小的碎片，向各个方向迸射；这些碎片的初始速率均为20 m/s。
我们假定碎片移动时不受空气阻力，但处在均匀的重力场中，重力加速度g=9.81 m/s2。
求碎片在落地前所经过空间的总体积（单位为m3）。将你的答案四舍五入到四位小数。