Question

A body of mass $m$ hits normally a rigid wall with velocity $v$ and bounces back with the same velocity. The impulse experienced by the body is:

• A. Zero
• B. $1mv$
• C. $1.5mv$
• D. $2mv$

Answer 1

Answer: (D)

$2mv$

Let initially the body is moving along positive x- axis with speed $v$.

So, momentum of the body initially $\overrightarrow{p_i}=mv\hat{i}$

After bouncing back, the body moves along negative x-axis with same speed.

So,momentum of the body finally $\overrightarrow{p_f}=-mv\hat{i}$

Thus change in momentum of body $\Delta \overrightarrow{p}=\overrightarrow{p_f}-\overrightarrow{p_i}=-2mv\hat{i}$

Impulse experienced $\overrightarrow{I}=\Delta \overrightarrow{p}=-2mv\hat{i}$

$⟹|\overrightarrow{I}|=2mv$