Question

Two carts, a and b, are connected by a rope 39 ft long that passes over a pulley p. 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? (round your answer to two decimal places.)

Answer 1

I've added an attachment to this post to explain the problem. Two carts, A and B, are connected by a rope 39 feet long that passes over a pulley P. The point Q is on the floor h = 12 ft directly beneath P and between the carts. Cart A is being pulled away at a speed of 2.5 ft/s. How fast is cart B moving toward Q at the instant when cart A is 5 ft from Q. (round to 2 decimal places) From the problem, I know the following things: PQ = h = 12 AQ = 5 AP = 13 (by Pythagoras) APB = 39 PB = 39-13 = 26 QB = 2\sqrt{133} (by Pythagoras) (work to follow in next posting for organization)