Question

A bulb is placed at the centre of a circular track of radius $10m$. A vertical wall is erected touching the track at a point P. A man is running along the track with a speed of $10m/\sec$. Starting from $P$ the speed with which his shadow is running along the wall when he is at an angular distance of $60^{\circ }$ from $P$ is

• A. 30 m / sec
• B. 40 m / sec
• C. 60 m / sec
• D. 80 m / sec

Answer 1

Answer: (B)

$\vec{v}=r\frac{d\theta }{dt}=10$
$\tan \theta =\frac{y}{r}$
or, $y=r\tan \theta$
or, $\frac{dy}{dt}=r{\sec }^2\theta \cdot \frac{d\theta }{dt}$
$=10\times {\sec }^2\left(60^{\circ }\right)=40m/\sec$