# A car is fitted with a convex side-view mirror of focal length 20 cm. A second car 2.8 m behind the first car is overtaking the first car at a relative speed of 15 m s-1. The speed of the image of the second car as seen in the mirror of the first one is Option 1) $\frac{1}{10}ms^{-1}$ Option 2) $\frac{1}{15}ms^{-1}$ Option 3) $10\: ms^{-1}$ Option 4) $15\: ms^{-1}$

P Prateek Shrivastava

As we learnt in

Mirror Formula -

$\frac{1}{v}+\frac{1}{u}=\frac{1}{f}$

- wherein

$u=$ Object distance from pole of mirror.

$v=$ Image distance from pole of mirror.

$f=$ focal length of the mirror.

From mirror formula

$\frac{1}{v}+\frac{1}{u}=\frac{1}{f}$

so,  $\frac{dv}{dt}=-\frac{v^{2}}{u^{2}} \left(\frac{du}{dt} \right )$

$\frac{dv}{dt}=\left(\frac{f}{u-f} \right )^{2}\frac{dv}{dt}$

$\Rightarrow\ \; \frac{dv}{dt}=\frac{1}{15}ms^{-1}$

Correct option is 2.

Option 1)

$\frac{1}{10}ms^{-1}$

This is an incorrect option.

Option 2)

$\frac{1}{15}ms^{-1}$

This is the correct option.

Option 3)

$10\: ms^{-1}$

This is an incorrect option.

Option 4)

$15\: ms^{-1}$

This is an incorrect option.

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