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 overtake the first car at a relative speed of 15 m/s, then how fast will the image be moving?

Options

A. 0.016 m/s
B. 0.0257 m/s
C. 0.162 m/s
D. 0.0072 m/s

Answer

A

Explanation

Mirror formula `(1)/(v) + (1)/(u) = (1)/(f)`
Differentiataing w.r.t.t,
`O = (1)/(v^(2)) (dv)/(dt)-(1)/(u^(2)) (du)/(dt)`
(as focus length is constant)
`(dv)/(dt) = (v^(2))/(u^(2)) (du)/(dt)`
but Now, `(1)/(v)=((1)/(20)+(1)/(600))`
`therefore v = (600)/(31) cm`
and `(v)/(u) = (600//31)/(600) = (1)/(31)`
Speed of image `=(dv)/(dt)=-((1)/(31))^(2)xx15`
= 0.016m/s