Question

A car is fitted with a convex side-view mirror of focal length $20 \,cm$. A second car $2.5\, m$ 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 mirror of the first one is

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

Answer 1

Answer: (C)

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