Question

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

• A. $1\text{m/s}$
• B. $0.1\text{m/s}$
• C. $2\text{m/s}$
• D. $2.5\text{m/s}$

Answer 1

The correct option is B $0.1\text{m/s}$

Mass of the bullet , $m_1=20\text{g}=0.02\text{kg}$
Total mass of man $m_2=80\text{kg}$
Initial velocity of the bullet , $u_i=400\text{m/s}$
Final velocity of the bullet, $u_f=0\text{m/s}$
Let the velocity of man with which he falls is $v_f$

We know that in the process of collision external force applied on the system is zero. Therefore, the momentum of system remains conserved.
$\Rightarrow p_i=p_f$
$\Rightarrow 0.02\times 400+0=0+80\times v_f$
$\Rightarrow v_f=\frac{400\times 0.02}{80}$
$\Rightarrow v_f=0.1\text{m/s}$