Question

A car is fitted with a convex side-view mirror of focal length $20cm$. A second car $2.8m$ 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. $\frac{1}{10}m/s$
• B. $\frac{1}{15}m/s$
• C. $10m/s$
• D. $15m/s$

Answer 1

Answer: (B)

$\frac{1}{15}m/s$

Given,

Focal length, $f=20cm$

Speed = 15 m/s.

From mirror formula, $\frac{1}{v}+\frac{1}{u}=\frac{1}{f}$

Differentiating on both sides wrt to t,

$-\frac{1dv}{v^{2}dt}-\frac{1du}{u^{2}dt}=0$

$\frac{dv}{dt}=15(\frac{280}{15\times 280}{)}^2$

$v\cong \frac{1}{15}m/s$