Question

An observer moves towards a stationary plane mirror at a speed of $4m/s$ the speed of image with respect to mirror is __________

Answer 1

Step 1: Given data

An observer moves towards a stationary plane mirror at a speed of $4m/s$

Step 2: Find the speed of the image with respect to the mirror

The mirror and the object move toward each other As a result, there is a relative velocity between the object and the mirror. Similarly, the image will move toward the mirror in a manner that is comparable to that of the object. The relative velocity of the image in relation to the mirror allows us to calculate its relative velocity in relation to the ground.

Let the velocity of the observer with respect to the mirror be, $v_{om}=-4m/s$

$-\frac{dx}{dt}$ As the observer approaches the mirror facing away from the negative $x-$ axis

Let the velocity of the image with respect to the mirror be, $v_{im}=4m/s$

$x\text{'}=x$

$$\begin{gathered} v_{im}=\frac{dx\text{'}}{dt}=\frac{dx}{dt}\left[\because x\text{'}=x\right] \\ =4m/s \end{gathered}$$

Now,

$$\begin{gathered} \therefore v_{io}=v_{im}+v_{mo} \\ \Rightarrow v_{io}=v_{im}-v_{om} \\ =4-\left(-4\right) \\ =8m/s \end{gathered}$$

Hence the answer is $8m/s$

An observer moves towards a stationary plane mirror at a speed of $4m/s$ the speed of image with respect to mirror is $8m/s$