Question

A racing car is travelling along a track at a constant speed of $60m{s}^{-1}$. A television cameraman is recording the event from a distance of $30m$ directly away from the track as shown in the figure. In order to keep the car under view at the situation shown in the figure, find the angular speed at which the camera should be rotated?

• A. $1rad{s}^{-1}$
• B. $\frac{1}{2}rad{s}^{-1}$
• C. $2rad{s}^{-1}$
• D. $\frac{1}{4}rad{s}^{-1}$

Answer 1

Answer: (B)

$\frac{1}{2}rad{s}^{-1}$

From triangle, let at anytime it make an angle $\theta$

$l=a\times tan\theta$

Now differentiate with respect to time

$\frac{dl}{dt}=a\frac{d\left(tan\theta \right)}{dt}$

$v=a\times se{c}^2\left(\theta \right)\times \omega$,

Now $\theta ={60}^{o}v=60m/s$

$\omega =0.5rad{s}^{-1}$