Hello, topher0805!

LetTwo carts, A and B, are connected by a rope 43 ft long that passes over a pulley P.

The point Q is on the floor; h = 14 ft directly beneath P and between the carts.

Cart A is being pulled away from Q at a speed of 2 ft/s.

How fast is cart B moving toward Q at the instant when cart A is 5 ft from Q?

In right triangle

In right triangle

The length of the rope is: .

. . So we have: .

Differentiate with respect to time:

. .

Hence, we have: .

We are given: . ft/sec

Substitute into [1] and solve for

Then substitute all that into [2].

. .Bon voyage!