Question

A racing car is travelling along a straight track at a constant velocity of $40\text{m/s}$. 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 the camera should be

• A. $3\text{rad/s}$
• B. $2\text{rad/s}$
• C. $4\text{rad/s}$
• D. $1\text{rad/s}$

Answer 1

The correct option is D $1\text{rad/s}$


From the figure, horizontal distance travelled by the car
$x=30\tan \theta$
$\therefore \left(\frac{dx}{dt}\right)=30{\sec }^2\theta )\cdot \frac{d\theta }{dt}$
or $v_{car}=\left(30{\sec }^2\theta \right)\omega$
$\therefore \omega =\frac{v_{car}}{30{\sec }^2\theta }$
$=\frac{40}{\left(30\right){\sec }^2{30}^{\circ }}=1\text{rad/s}$