Question

Superman is trapped in a planet full of evil superman clones, who are as strong as him! As he tries to flee the planet, unknown to him, there is a huge plane reflector suspended in the sky. As he zooms upward at 100 m/s, how fast will he see his image (which, he will mistake to be an evil clone!) zoom towards him? (The reflector is at rest, and very very far from superman at the instant.)

• A. $100\frac{m}{s}$, away from him.
• B. $200m/s$, towards him.
• C. $100m/s$, towards him.
• D. $200\frac{m}{s}$, away from him.

Answer 1

The correct option is B $200m/s$, towards him.

As the plane reflector is 'very very far' from superman, he can be considered to be a point object! Below is the diagram representing this scenario:

Remember, velocities are vectors, and how do we denote their direction in 1-D motion? Yup, by assigning one of the possible directions as positive, and the other as negative. So, before we start talking about velocities, let us take up as positive and down as negative. Now, Superman is moving upwards, towards the mirror, so, in our diagram the point object 'O' representing him is moving up, hence, it's velocity with respect to a stationary observer is, $\overrightarrow{v_o}=+100m/s$.
Further, the image moves with equal and opposite velocity as seen from the mirror, also here the mirror is stationary, so, the velocity of the image with respect to it is same as the velocity with respect to any stationary observer, that is $100m/s$ downwards, $\overrightarrow{v_I}=-100m/s$.
We need to find the velocity of the image with respect to the object,$\overrightarrow{v_{I,O}}=\overrightarrow{v_I}-\overrightarrow{v_o}$(recall how relative velocity is worked out).
Therefore, $\overrightarrow{v_{I,O}}=-100\frac{m}{s}-(+100\frac{m}{s})=-200\frac{m}{s}$
Which, as per our definition of '+' and '-' means it moves
200 m/s downwards, that is towards the object. Hence, Superman will think his evil clone is moving towards him with a speed of $200\frac{m}{s}$.