# A man wearing a bulletproof 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 the velocity of the man?

Nov 18, 2015

$\text{0.1 m/s}$

#### Explanation:

$m$ - mass of bullet $= \text{ 0.02 kg}$
$M$ - mass of man $= \text{ 80 kg}$
$u$ - initial velocity of bullet $= \text{ 400 m/s}$
$U$ - initial velocity of man $= \text{0 m/s}$
$v$ - final velocity of bullet $= \text{ 0 m/s}$
$V$ - final velocity of man

Using conservation of momentum,

$\text{initial momentum " = " final momentum}$

$m \cdot u + M \cdot U = m \cdot v + M \cdot V$

$0.02 \cdot 400 + 80 \cdot 0 = 0.02 \cdot 0 + 80 \cdot V$

$8 = 80 \cdot V \implies V = \text{0.1 m/s}$

Therefore, the man moves with a velocity of $\text{0.1 m/s}$