Question

A convex driving mirror of focal length 20 cm, is fitted in a motor car. If
the second car 2 m broad and 1.6 m high is 6 m away from first car and
overtakes the first car at a relative speed of 15 m/s, then how fast will the
image be moving?
(1) 0.016 m/s (2) 0.0257 m/s (3) 0.162 m/s (4) 0.0073 m/s

Answer 1

Answer:

0.016m/s  

0.0257m/s

0.162cm

0.0073m/s

Explanation:

Solution :

(a) Mirror formula 1v+1u=1f

Differentiating w.r.t we get

0=−1v2dvdt−1u2dudt

dudt=−v2u2dudt

But dudt=15m/s

Now 1v=(120+1600)

∴v=600−31cm and vu=60031600=131

∴ Speed of image =dvdt=−(131)2×16=0.016m/s