Question

A racing car is travelling along a straight track at a constant velocity of $40m/s$ A fixed TV camera is recording the event as shown in figure. In order to keep the car in view, in the position shown, the angular velocity of camera should be

• A. $3$ rad/s
• B. $2$ rad/s
• C. $4$ rad/s
• D. $1$ rad/s

Answer 1

Answer: (D)

$1$ rad/s

$x=30\tan \theta$
$\therefore \left(\frac{dX}{dt}\right)=\left(30{\sec }^2\theta \right)\cdot \frac{d\theta }{dt}$
or $v_{car}=\left(30{\sec }^2\theta \right)\omega$
$\therefore \omega =\frac{v_{car}}{30{\sec }^2\theta }$
$=\frac{40}{\left(30\right)se{c}^2{30}^{\circ }}=1rad/s$