Please answer this question showing precise calculations Look at the following d

Question

Please answer this question showing precise calculations

Look at the following diagram: Here is what the diagram represents: C is the location of a speed camera, placed 5 metres above the road (directly above A). V is a fixed position 2.5 metres away from A. The camera tracks a moving vehicle as it passes V, going towards B. As the vehicle goes, the angle theta changes, and the faster the vehicle goes, the faster the angle changes. The speed limit of 50 km/h (kilometres per hour) corresponds to a critical angular velocity d theta/dt. If the vehicle goes above 50 km/h, then the angular velocity will be above critical, and the speed camera will take a picture of the vehicle. Find the critical angular velocity d theta/dt, in radians per second.

Explanation / Answer

AV / AC = tan(theta)

AV = AC*tan(theta)

differntiating

v = AC*sec^2 (theta) d(theta)/dt

d(theta)/dt = v*cos^2(theta)/AC

AC = 5 m

v = 50 kmph = 50*1000/3600 m/s

cos(theta) = 5/sqrt(5^2+2.5^2)

d(theta)/dt = (50*1000/3600)*(25/(5^2+2.5^2))/5 = 2.22 rad /s

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