Question

A bulb is placed at the centre of a circular track of radius $10 \,m$. A vertical wall is erected touching the track at a point P. A man is running along the track with a speed of $10\, m / \sec$. 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)

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