A racing car is travelling along a track at a constant speed of 40 m/s. A television cameraman is recording the event from a distance of 40 m directly away from the track as shown in figure. In order to keep the car under view, the camera is rotated with a certain angular velocity. This angular velocity should be

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1.0 rad/s

5 rad/s

0.5 rad/s

2.0 rad/s

answer is C.

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Detailed Solution

$\large {v_T} = r\omega$

$\large v\cos 45 = \left( {\frac{d}{{\cos 45}}} \right)\omega$

$\large \omega = \frac{v}{d}{\cos ^2}45 = 0.5{\text{ }}rad{\text{ }}{s^{ - 1}}$
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