Question

A person runs with a speed $u$ towards a bicycle moving away from him with speed $v$. The person approaches his image in the plane mirror fixed at the bicycle with a speed of :

• A. $u-v$
• B. $u-2v$
• C. $2u-v$
• D. $2(u-v)$

Answer 1

The correct option is D $2(u-v)$

The relative velocity of the person with respect to the bicycle = $u–v$
Assuming the mirror to be a plane mirror object distance = image distance
Thus, the velocity of the image w.r.t to the bicycle frame of reference will be = $(-(u-v\left)\right)$
Negative sign is there because the image moves opposite to the direction of the bicycle’s motion.
Therefore velocity of the image with respect to the person will be $(u–v)–\left(–(u–v)\right)=2(u–v)$