Question

A plane mirror is placed in yz plane facing towards negative x axis. The mirror is moving parallel to y axis with a speed of 5 cm/s. A point object P is moving in front of the mirror with a velocity $3cm/s\overline{i}+4cm/s\overline{j}+5cm/s\overline{k}$ . The velocity of image respect to mirror is :

• A. $-3cm/s\overline{i}+4cm/s\overline{j}+5cm/s\overline{k}$
• B. $-3cm/s\overline{i}-1cm/s\overline{j}+5cm/s\overline{k}$
• C. $-3cm/s\overline{i}-4cm/s\overline{j}-5cm/s\overline{k}$
• D. $3cm/s\overline{i}-4cm/s\overline{j}-5cm/s\overline{k}$

Answer 1

The correct option is B $-3cm/s\overline{i}-1cm/s\overline{j}+5cm/s\overline{k}$

Let the velocities of the object and the image with respect to mirror be $V_u$ and $V_v$ respectively.

Velocity of the mirror is $5cm/s\overline{j}$

$V_u=(3\overline{i}+4\overline{j}+5\overline{k})-\left(5\overline{j}\right)cm/s=(3\overline{i}-1\overline{j}+5\overline{k})cm/s$

Components of $V_u$ and $V_v$ parallel to the mirror are same.

Therefore ${V_v}^{\parallel }=(-1\overline{j}+5\overline{k})cm/s$

Components of $V_u$ and $V_v$ perpendicular to the mirror are equal in magnitude but opposite in direction.. Therefore ${V_v}^{\perp }=(-3\overline{i})cm/s$

Therefore, velocity of the image with respect to the mirror is:
$V_v=(-3\overline{i}-1\overline{j}+5\overline{k})cm/s$