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. `15 m//s`
D. `(1)/(10)m//s`

Answer

A

Explanation

`f=+20cm`
`u=-2.8m=-280cm`
`v_("relative")=+15m//s`

The position of image
`(1)/(v)+(1)/(u)=(1)/(f)`
`(1)/(v)-(1)/(2.8)=(10)/(2)`
`(1)/(v)=5+(10)/(28)`
`(1)/(v)=(70+5)/(14)`
`"Image of second car at distance v"=+(14)/(75)m`
`(1)/(v)+(1)/(u)=(1)/(f)`
`U.=(dv)/(dt)="Speed of image formed in car 1"`
`-(1)/(v^(2))(dv)/(dt)-(1)/(u^(2))(du)/(dt)=0`
`V.=(-du.)/(dt)="Speed of object (cars)"`
`(-V.)/(v^(2))=(U.)/(u^(2))`
`U.=15m//s`
`"Velocity of image, "V.=(v^(2))/(u^(2))U.`
`=-((14)/(75))^(2)xx(1)/((2.8)^(2))xx15`
`=-(14xx14)/(75xx75)xx(10xx10)/(28xx28)xx15`
`V.=(-1)/(15)m//s`