Problem 317

Problem 317


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.


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