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. `10m//s`
C. `15m//s`
D. `1/10 m//s`

Answer

A

Explanation

From mirror formula `1/u+1/v=1/f`
`implies -1/(u^(2)) (du)/(dt)-1/(v^(2)) (dv)/(dt)=0`
`implies(dv)/(dt)=-(v^(2))/(u^(2))((du)/(dt))`
But `v/u=f/(u-f)`
`:.(dv)/(dt)=-(f/(u-f))^(2) ((du)/(dt))`
`=(0.2/(-2.8-0.2))^(2)xx15=1/15ms^(-1)`