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Calculus/Releated rates, race car approaches camera

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Expert: - 11/14/2011


Question
You are videotaping a race from a stand 132ft from the track. You are following a car racing at 180mph(264ft/sec. How fast is the camera's angle changing when the car is right in front of you?

Answer
The relation is given by tanA = x/y, where the track is y feet away, the distance of the car from being straight out is x, and A is the angle.

The derivative is sec˛A dA/dt = (1/y) dx/dt.

Since the car is 132' away, and that is y, and it is moving at 264f/s, and that is dx/dt,
and it is straight in front, which says A = 0, the equation breaks down to
1˛ dA/dt = (1/132)264 , so dA/dt = 2.

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