Calculus help please

Question

2. A boat is being pulled into a dock by a rope attached to it and passing through a pulley on the deck, positioned 6 meters higher than the boat. If the rope is being pulled in at a rate of 3 meters/sec, how fast is the boat approaching the dock when it is 8 meters from the dock? Make sure your answer includes units.

Answer 1

Suppose s is distance from the boat to the pulley

Then if x is the distance to the dock L s² = 6² + x²

We need to find dx/dt when ds/dt = -3, and when x = 8

2s ds/dt = 2x dx/dt

when x = 8, s = sqrt (36 + 64) = 10

So 2 . 10 . -3 = 2 . 8 . dx/dt

dx/dt = -60/16 = -3.75

So the boat is approaching the dock at 3.75 m/s, when it is 8 m from the dock