Question

A plane mirror is moving with velocity $4\hat{i}+5\hat{j}+8\hat{k}$. A point object in front of the mirror moves with a velocity $3\hat{i}+4\hat{j}+5\hat{k}$ Here $\hat{k}$ is along the normal to the plane mirror and facing towards the object. The velocity of the image is-

• A. $-3\hat{i}-4\hat{j}+5\hat{k}$
• B. $3\hat{i}+4\hat{j}+11\hat{k}$
• C. $-4\hat{i}+5\hat{j}+11\hat{k}$
• D. $7\hat{i}+9\hat{j}+11\hat{k}$

Answer 1

Answer: (B)

$3\hat{i}+4\hat{j}+11\hat{k}$

The velocity of plane mirror $=4\hat{i}+5\hat{j}+8\hat{k}$

Point Velocity $=3\hat{i}+4\hat{j}+5\hat{k}$

Velocity along normal changes but velocity $\perp$ to normal remain constant.

${\overrightarrow{V}}_{alongnormal}={\overrightarrow{V}}_{Im\overrightarrow{K}}=\left(2\right)\left(8\right)-\left(5\right)$

$\therefore \overrightarrow{V}=+[3\hat{i}+4\hat{j}]+11\hat{k}$