The traffic police has installed Over Speed Violation Detection (OSVD) system at various locations in a city. These cameras can capture a speeding vehicle from a distance of 300 m and even function in the dark.
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A camera is installed on a pole at the height of 5 m. It detects a car travelling away from the pole at the speed of 20 m/s. At any point, \(x\) m away from the base of the pole, the angle of elevation of the speed camera from the car C is \(\theta\).
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On the basis of the above information, answer the following questions:
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Express \( \theta \) in terms of the height of the camera installed on the pole and \( x \).
Find \( \frac{d\theta}{dx} \).
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Find the rate of change of angle of elevation with respect to time at an instant when the car is 50 m away from the pole.
OR If the rate of change of angle of elevation with respect to time of another car at a distance of 50 m from the base of the pole is \( \frac{3}{101} \) rad/s, then find the speed of the car.
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