Question

A man $(\text{mass}=50\text{kg})$ and his son $(\text{mass}=20\text{kg})$ are standing on a frictionless surface facing each other. The man pushes his son so that he starts moving at a speed of $0.70{\text{ms}}^{-1}$ with respect to the man. The speed of the man with respect to the surface is:

• A. $0.20{\text{ms}}^{-1}$
• B. $0.47{\text{ms}}^{-1}$
• C. $0.14{\text{ms}}^{-1}$
• D. $0.28{\text{ms}}^{-1}$

Answer 1

The correct option is A $0.20{\text{ms}}^{-1}$

Let $v_{sm}$ be the velocity of son with respect to man,
$v_m$ and $v_s$ be the velocity of man and son respectively with respect to surface.

As the son and the man will be moving in opposite direction,
$v_{sm}=v_s+v_m$

$v_s=0.7-v_m$

According to conservation of momentum,

$P_i=P_f$

$\Rightarrow P_i=m_s{v}_s-m_m{v}_m$

$\Rightarrow 0=20(0.7-v_m)-50v_m$

$\Rightarrow 70v_m=14$

$\Rightarrow v_m=0.2{\text{ms}}^{-1}$

Hence, option $\left(B\right)$ is correct.