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}

 

Answers (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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