Question

An object is approaching a fixed plane mirror with velocity $10\text{m/s}$ making an angle of ${60}^{\circ }$ with the normal to the mirror. The speed of image with respect to the mirror is

• A. $15\text{m/s}$
• B. $10\text{m/s}$
• C. $20\text{m/s}$
• D. $25\text{m/s}$

Answer 1

The correct option is B $10\text{m/s}$

We know that for fixed plane mirror,
$\left(1\right)$ Perpendicular to the mirror, $v_o=-v_i$
$\left(2\right)$ Parallel to the mirror, $v_o=v_i$
This means that the magnitude of the velocity of the image is equal to the magnitude of the velocity of the object along the perpendicular and parallel to the mirror.
Thus, the speed of image is equal to the speed of object because $v=\sqrt{v_{\perp }^2+v_{\parallel }^2}$

Hence, the speed of the image is $10\text{m/s}$.