Question

For the situation shown in the figure, find the velocity of the image formed by the mirror.

• A. $5(1+\sqrt{3})\hat{i}+5\sqrt{3}\hat{j}\text{m/s}$
• B. $5(1+\sqrt{3})\hat{i}-5\sqrt{3}\hat{j}\text{m/s}$
• C. $-5(1+\sqrt{3})\hat{i}+5\sqrt{3}\hat{j}\text{m/s}$
• D. $-5(1+\sqrt{3})\hat{i}-5\sqrt{3}\hat{j}\text{m/s}$

Answer 1

The correct option is C $-5(1+\sqrt{3})\hat{i}+5\sqrt{3}\hat{j}\text{m/s}$

Let, $v_i=$ velocity of image
$v_o=$ velocity of object
$v_m=$ velocity of mirror

Along $x-$ direction, we can write
$v_{ix}-v_{mx}=-(v_{ox}-v_{mx})$
$\Rightarrow v_{ix}-(-5\cos {30}^{\circ })=-(10\cos {60}^{\circ }-(-5\cos {30}^{\circ }\left)\right)$
$\therefore v_{ix}=-5(1+\sqrt{3})\text{m/s}$

Along $y-$ direction,
$v_{iy}=v_{oy}$
$\Rightarrow v_{iy}=10\sin {60}^{\circ }=5\sqrt{3}\text{m/s}$

$\therefore$ Velocity of the image
$\overrightarrow{v_i}=-5(1+\sqrt{3})\hat{i}+5\sqrt{3}\hat{j}\text{m/s}$