Question

A car is fitted with a convex side view mirror of focal length 20cm. A second car 2.8m behind the car is overtaking the first car is a relative speed of 15m/s. The speed of the image of the second car as seen in the mirror of the first one is?

(a) 1/15 m/s 

(b) 10 m/s 

(c) 15 m/s 

(d) 1/10 m/s

Answer 1

Correct option is (a) 1/15 m/s

Explanation:

1/u + 1/v = 1/f Gives            

- (1/u2)(du/dt) –(1/v²)(dv/dt) = 0 

dv/dt = -(v²/u²)(du/dt) but v/u = f/(u-f) 

dv/dt = -[f/(u-f)]2(du/dt) 

= {0.2/(-2.8-0.2)}2* 15              

= 1/15 ms^-1