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Two carts, A and B, are connected by a rope 39 ft long that passes over...

Two carts, A and B, are connected by a rope 39 ft long that passes over a pulley P (see the figure). The point Q is on the floor h = 12 ft directly beneath P and between the carts. Cart A is being pulled away from Q at a speed of 3 ft/s. How fast is cart B moving toward Q at the instant when cart A is 5 ft from Q? Answer should be in ft/sec.

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Its a related rate problem, we need find the instant rate of cart B when the cart A is moving away from the point Q with speed of 3 ft/s, thats our objective of this problem. So, first lets draw a geometrical di agram with the given information and get the details of it as below 12ft See the diagram there are two right angle triangles APQ and BPQ .Use the Pythagorean theorem to find the lengths of AP and BP and add them out and equate to the actual length of the rope which is 39 ft. +12 +w2 +12-39 Differentiate the equation with respect to the time t and get the below +122 +122)4(39) dt 242 +12 d +12 ar хах, ydy

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