Question

A car is fitted with a convex side-view mirror of focal length $20cm$. A second car $2.5m$ behind the first car is overtaking the first car at a relative speed of $15m/s$. The speed of the image of the second car as seen in the mirror of the first one is

• A. $15m/s$
• B. $\frac{1}{10}m/s$
• C. $\frac{1}{15}m/s$
• D. $10m/s$

Answer 1

Answer: (C)

For mirror
$\frac{1}{v}+\frac{1}{u}=\frac{1}{f}$
$\frac{-1}{v^2}\frac{dv}{dt}-\frac{1}{u^2}\frac{du}{dt}=0$
$\frac{dv}{dt}=\frac{-v^2}{u^2}\frac{du}{dt}=-{\left(\frac{f}{f-u}\right)}^2\frac{du}{dt}$
$=-{\left(\frac{20}{20+280}\right)}^2\frac{du}{dt}$
$={\left(\frac{1}{15}\right)}^2\frac{du}{dt}=\frac{1}{15}m/s$