Question

A man of mass m is standing on a stationary wooden board of mass M kept on smooth ice. The man starts running on the board and acquires a speed u relative to the board. Find the speed of the man relative to stationary observer. The board is long enough.

• A.
• B.
• C.
• D.

Answer 1

The correct option is B

The system is initially at rest. Hence its momentum is zero. Since no external force is acting on the system. Therefore momentum of the system will remain zero. Considering in X - direction, the momentum of the system (man + board) should be zero.

Given velocity of the man with respect to board, ${\overrightarrow{v}}_{mb}=u\hat{i}$

Let velocity of the board, ${\overrightarrow{v}}_b=v_b\hat{i}$

Hence velocity of the man, ${\overrightarrow{v}}_m={\overrightarrow{v}}_{mb}+{\overrightarrow{v}}_b$

$=u\hat{i}+v_b\hat{i}=(u+v_b)\hat{i}$

$M{\overrightarrow{v}}_b+m{\overrightarrow{v}}_m=0$

$M{v}_b\hat{i}+m(u+v_b)\hat{i}=0$ $\Rightarrow$ $v_b=-\frac{mu}{m+M}$

Velocity of the man ${\overrightarrow{v}}_m=(u-\frac{mu}{m+M})\hat{i}$ , ${\overrightarrow{v}}_m=\frac{Mu}{m+M}\hat{i}$