Question

A racing car is traveling along a track at a constant speed of 40m/s. A TV cameraman is recording the event from a distance of 30 m directly away from the track as shown in figure in order to keep the car under view, at what angular speed must the camera be rotated [in rad/sec]:

• A. 1
• B. 3
• C. 5
• D. 4

Answer 1

The correct option is B

3

In $\Delta ABC$
$tan\varphi =\frac{x}{h}x=htan\varphi$
differentiates w.r.t. time
$\frac{dx}{dt}=hse{c}^2\varphi \frac{d\varphi }{dt}[\frac{d\left(tan\varphi \right)}{dt}=se{c}^2\varphi ]v=hse{c}^2\varphi \omega \omega =\frac{v}{hse{c}^2\varphi }\omega =\frac{vco{s}^2\varphi }{h}\omega =\frac{40}{30}co{s}^{2}30=\frac{40}{30}\times {\left(\frac{\sqrt{3}}{2}\right)}^2=1rad/sec$