Question

A ball moving with a momentum of $5\text{kg m/s}$ strikes against a wall at an angle of 45° and is reflected at the same angle. Calculate the change in momentum (in magnitude).

• A. $7.07\text{kg m/s}$
• B. $14.04\text{kg m/s}$
• C. $3.53\text{kg m/s}$
• D. $28.08\text{kg m/s}$

Answer 1

The correct option is A $7.07\text{kg m/s}$

Let $\overrightarrow{P_1}$ and $\overrightarrow{P_2}$ be the initial and final momenta respectively of the ball.
Change in momentum $=\overrightarrow{P_2}-\overrightarrow{P_1}=\overrightarrow{P_2}+(-\overrightarrow{P_1})=\overrightarrow{AB}$
From the figure

$AB=\sqrt{P_1^2+P_2^2}=\sqrt{5^2+5^2}{\text{kg ms}}^{-1}$ or $AB=\sqrt{50}{\text{kg ms}}^{-1}=7.07{\text{kg ms}}^{-1}$