Question

A person walks at a velocity $v$ in a straight line forming an angle $\alpha$ with the plane of a plane mirror. the velocity at which he approaches his image is:

• A. $v$
• B. $v\sin \alpha$
• C. $2v\sin \alpha$
• D. $2v\cos \alpha$

Answer 1

The correct option is D $2v\cos \alpha$

• Since it is a plane mirror vertical component of velocity have no significance.
  
• The person approaches the mirror with a horizontal speed of $v\cos \alpha$.
  
• Hence his image also move towards the mirror with same velocity $v\cos \alpha$ in the opposite direction.
• Velocity at which he approaches his image is ,$v^{\prime }=v\cos \alpha -(-v\cos \alpha )=2v\cos \alpha$