A train is traveling 0.9 km/min along a straight track, moving in the direction as shown in the figure below. A movie camera, 0.5 km away from the track, is focused on the train. (a) How fast is the distance from the camera to the train changing when the train is 1 km from the camera? Round your answer to 3 decimal places. (b) How fast is the camera rotating at the moment when the train is 1 km from the camera? Round your answer to 3 decimal places.
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5 km), and the distance from the train to the point on the track closest to the camera (x). We have d^2 = x^2 + 0.5^2. Differentiating both sides with respect to time (t), we get 2d(dd/dt) = 2x(dx/dt). We know that dx/dt = -0.9 km/min (the train is moving towards Show more…
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