A plane mirror and an object approach each other with speeds of 5m/s and 10 m/s respectively. The speed of the image will be

The correct option is C. 20 m/s.

Given : Speed of the object = 10 $m/sec$

Speed of the mirror = 5 $m/sec$

Mirror and object are approaching each other.

To find:

Speed of image

Let initial position of object be at $x_{oi}=0$

Let initial position of mirror be at $x_{mi}=u$

Object distance equals the image distance. Hence, the initial position of the image is $x_{ii}=2u$

Distance is the product of speed and time.

After time $t$,

Position of object will be:

$x_{of}=x_{oi}+u_{o}t=5t$

Position of mirror will be:

$x_{mf}=x_{mi}-u_{f}t=u-10t$

Let the final position of image be $x_{if}$.

Using object distance equals image distance after time $t$,

$x_{if}-x_{mf}=x_{mf}-x_{of}$

$x_{if}=2u-25t$

Distance moved by image in time $t$ is:

$s_i=x_{if}-x_{ii}$

$s_i=-25t$

Speed is the ratio of distance and time. Speed of the image is:

$v_i=\frac{s_i}{t}=-25m/s$

Negative sign appears because image is moving leftwards.

Hence, speed of image is $25m/s$.