Question

A point object approaches a plane mirror with a
need of 10 ms , while the image recedes away
from the mirror with a speed of 6 ms. The direction
and magnitude of the velocity of mirror is :-​

Answer 1

If x is the distance between the object and the mirror, 2x is the distance between the object and its image because for a plane mirror object distance is equal to the image distance. So if the plane mirror is approaching the object with a speed of x/t, then the image will approach the object with a speed of 2x/t. So if x/t = 10 cm/s, 2x/t = 20 cm/s. Hence the image will approach you with a speed of 20 cm/s.

Answer 2

The mirror is moving away from the object with a magnitude of velocity 2 m/s.

Explanation:

We are given that:

• Speed of mirror = 10 m/s
• Image recedes away from the mirror with speed = 6 m/s
• To find: Direction and magnitude of velocity

Solution:

The magnitude of the velocity of mirror is =  10 - 6 / 2

Magnitude of velocity = 4 / 2

Magnitude of velocity = 2 m/s

Thus the mirror is moving away from the object with a magnitude of velocity 2 m/s.