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

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(2) $2 rad / s$

(3) $4 rad / s$

(1) $3 rad / s$

(4) $1 rad / s$

answer is D.

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Detailed Solution

$x = 30 tanθ$

$∴ (\frac{dX}{dt}) = (30 \sec^{2} θ) \cdot \frac{dθ}{dt} v_{car} = (30 \sec^{2} θ) ω ∴ ω = \frac{v_{car}}{30 \sec^{2} θ} = \frac{40}{(30) \sec^{2} 30 °} = 1 rad / s$

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