Question

A man wearing a bullet-proof vest stands still on roller skates. The total mass is 80 kg. A bullet of mass 20 grams is fired at 400 m/s. It is stopped by the vest and falls to the ground. What is then the velocity of the man?

Answer 1

Here, mass of bullet = 20 g
$$\begin{gathered} =\frac{20}{1000}\mathrm{kg} \\ =0.02\mathrm{kg} \end{gathered}$$
Velocity of bullet = 400 m/s
Momentum of the bullet before hitting the man is = (0.02)(400) = 8 kg.m/s
After hitting the man the bullet stops and falls on the ground.
Mass of mass, M = 80 kg
If v is the velocity of the man after being hit by the bullet then,
Mv = 8
⇒ v = 8/80 = 0.1 m/s
This is the required velocity of the man.