Question

An object is approaching a fixed plane mirror with velocity $5\text{m/s}$ making an angle of ${45}^{\circ }$ with the normal. The speed of image with respect to mirror is

• A. $5\text{m/s}$
• B. $\frac{5}{\sqrt{2}}\text{m/s}$
• C. $5\sqrt{2}\text{m/s}$
• D. $10\text{m/s}$

Answer 1

The correct option is A $5\text{m/s}$


As shown in the figure, the direction of the component of velocity normal to the plane of the mirror gets reversed. While the component in the direction parallel to the plane of the mirror remains same. The magnitude of each component remains same.
Speed of image with respect to mirror
$=\sqrt{\left(\frac{5}{\sqrt{2}}\right)+\left(\frac{5}{\sqrt{2}}\right)}=5\text{m/s}$
Hence, the correct answer is option (a).

Why this question? Concept: When the object moves with speed u towards (or away) from the plane mirror then image also moves toward (or away) with speed $u$. But relative speed of image w.r.t. object is $2u$.