Question

Man X is standing in front of the plane mirror while man Y is running towards him from behind. If the man Y is running at a speed of $1m{s}^{-1}$ , how many metres nearer does the manY seem to be away from man X after $5seconds$ ?

(A) $7m$
(B) $5m$
(C) $6m$
(D) $10m$

Answer 1

Hint :In this question, it is given that the man Y is running in front of the mirror. We know that in the case of the plane mirror, the object distance and the image distance will be the same. As the man X is stationary the velocity of the man Y with respect to him is the same as that with respect to the mirror.

Complete Step By Step Answer:
We know that for plane mirrors, the image distance is the same as the object distance but in the opposite direction.
Therefore, if we consider u as object distance and v as the image distance, we can say that
 $\left|u\right|=\left|v\right|$
As per the definition of velocity, it is the distance covered during the unit time.
 $\Rightarrow \left|{\displaystyle \frac{du}{dt}}\right|=\left|{\displaystyle \frac{dv}{dt}}\right|$
Thus, the speed of image is equal to the speed of man Y.
As the man X is stationary, Hence, the speed of man Y with respect to man X will be $1m{s}^{-1}$ .
Thus, we can say that the speed of image of man Y with respect to the man X is:
 $1-\left(-1\right)=1+1=2m{s}^{-1}$
The distance covered by the image of man Y with respect to man X in $5seconds$ will be : $2\times 5=10m$ .
Thus, the man Y seems to be $10m$ away from man X after $5seconds$ .
Hence, option D is the right answer.

Note :
Here, we have used the concept of the relative velocity. In the case of a plane mirror, we have seen that the velocities of the image and the object have the same magnitude. However the directions of these velocities are opposite.