Question

A spot light $S$ rotates in a horizontal plane with a constant angular velocity of $0.1rad/s$. The spot of light $P$ moves along the wall at a distance $3m$. What is the velocity of the spot $P$ when $\theta ={45}^o$?

• A. $0.6m/s$
• B. $0.5m/s$
• C. $0.4m/s$
• D. $0.3m/s$

Answer 1

The correct option is A $0.6m/s$

$\text{Linear velocity},v=\frac{wr}{\sin \theta }$

If d is the distance from the spot light to wall

$r=\frac{d}{cos\theta }$

$=\frac{3}{\cos \left({45}^{\circ }\right)}$

$\text{velocity of the spot},v=\frac{lor}{\sin \theta }=\frac{0.1\times \frac{3}{\cos {45}^{\circ }}}{\sin {45}^{\circ }}$

$=0.6m{s}^{-1}$