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

Answer 1

The correct option is 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 remains constant
${\overrightarrow{V}}_{\text{image along normal}}=2V_m-V_o=(16-5)\hat{k}=+11\hat{k}$
${\overrightarrow{V}}_{\text{image perpendicular to normal}}=[3\hat{i}+4\hat{j}]$

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