A camera is located 10 meters from a straight road along which a car is travelli

Question

A camera is located 10 meters from a
straight road along which a car is travelling at
100 km/hour. The camera turns so that it is
pointed at the car at all times. In radians per
second, how fast does the camera turn at the
moment when the car is 50 meters from the point on the road nearest to the camera (i.e. when h = 50 m)?

Attached as image also:

A camera is located 10 meters from a straight road along which a car is travelling at 100 km/hour. The camera turns so that it is pointed at the car at all times. In radians per second, how fast does the camera turn at the moment when the car is 50 meters from the point on the road nearest to the camera (i.e. when h = 50 m)?

Explanation / Answer

in time 1sec, car travels = 100 *1000/3600 * 1 = 27.78 m

so now distance between car and camera = sqrt (50^2 + 27.78^2) = 57.2 m

so sin (theta) = 27.78 / 57.2 = 0.486

so theta = 29.08 degree

so rate of change of angle = 29.08 degree / sec

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