Answer to Question #102613 in Mechanics | Relativity for Fire

Question

A bullet is fired vertically upward with an initial velocity of 98m/s from the top of a building 100m high. Find
1. The maximum height reached above the ground
2. The total time before reaching the ground
3. The velocity on landing

Answer 1

1)

$$H=h+\frac{v^2}{2g}=100+\frac{98^2}{2(9.8)}=590\ m$$

2)

$$t_1=\frac{v}{g}=\frac{98}{9.8}=10\ s$$

$$t_2=\sqrt{\frac{2H}{g}}=\sqrt{\frac{2(590)}{9.8}}=11\ s$$

$$T=t_1+t_2=10+11=21\ s$$

3)

$$V=\sqrt{2gH}=\sqrt{2(9.8)(590)}=107.5\frac{m}{s}$$