Question

A bullet is fired vertically upward with an initial velocity of 98m/s from the top of a building 100m high. Find,

a) the maximum height reached above the ground

b) the total time before reaching the ground

c) the velocity on landing

Answer 1

Given:

$v_0=98\:\rm m/s$

$H=100\:\rm m$

a) the maximum height reached above the ground

$$H_{\max}=H+\frac{v_0^2}{2g}\\ =100+98^2/(2*9.8)=590\:\rm m$$

b) the total time before reaching the ground

$$y=-H-v_0t+gt^2/2$$

$$0=-100-98t+4.9t^2$$

$$t=21\:\rm s$$

c) the velocity on landing

$$v=\sqrt{v_0^2+2gH}\\ =\sqrt{98^2+2*9.8*100}=108\:\rm m/s$$