Here is a picture of the question with a better explaination of the problem. PLE

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Here is a picture of the question with a better explaination of the problem.

PLEASE DO NOT COPY FROM YAHOO ANSWERS OR ANYWHERE ELSE AS I HAVE ALREADY LOOKED AND THEY MAKE NO SENSE.

I WOULD ONLY POST HERE IF NO OTHER PLACE HAD A CLEAR AND CONCISE ANSWER (WHICH IS WHAT I AM HOPING FOR THANKS IN ADVANCE! :D)

A movie crew is working on a scene that involves filming a car moving at a high speed. For one perspective, a camera is positioned and fixed at a spot 50 feet from the car's path (see point C below). Construct a function s(rr) that determines the speed (in radians per second) at which the camera should turn to keep the car in frame when the car is at point B, which is x feet from the point on the path that is closest to the camera (point >1). Assume the car is moving at 90 miles per hour in the positive x direction. Be careful with the units.

Explanation / Answer

tan(theta) = x/50

sec^2(theta)d(theta) = dx/50

sec^2(theta)d(theta)/dt = (dx/dt)/50 = 132/50 = 2.64 (90mi/hr = 132ft/s)

d(theta)/dt = 2.64/sec^2(theta)

sec(theta) = sqrt(2500 + x^2)/50

sec^2(theta) = (2500 + x^2)/2500 = 1 + x^2/2500

s(x) = d(theta)/dt = 2.64/sec^2(theta) = 2.64*2500/(x^2 + 2500) = 6600/(x^2 + 2500)

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