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

Options

A. `- (1)/(15) m//s`
B. `10 m//s`
C. `15 m//s`
D. `(1)/(10) m//s`

Answer

A

Explanation

From mirror formula(using convex mirror)
`(1)/(u)+(1)/(v)=(1)/(f)`…(i)
Using `u = -2.8 m = -280 cm, f = 20 cm`
`:. (1)/(-280)+(1)/(v)=(1)/(20)` or `(1)/(v)=(1)/(20)+(1)/(280)=(15)/(280)`
or `v = (280)/(15) cm`
Differentiating (i) w.r.t. t, we have
`-(1)/(u^2)(du)/(dt)-(1)/(v^2)(dv)/(dt) = 0` or `(dv)/(dt)=-(v^2)/(u^2)((du)/(dt))`
`:.` Relative velocity of image,
`v_1=(dv)/(dt)= -(v^2)/(u^2)((du)/(dt)) = (-(280//15)^2)/(-280)^2 xx 15`
`=-(1)/(15) m//s`.