A boat is pulled into a dock by means of a rope attached to a pulley on the dock.....

Question

A boat is pulled into a dock by means of a rope attached to a pulley on the dock. The rope is attached to the front of the boat, which is 8 feet below the level of the pulley. If the rope is pulled through the pulley at a rate of 16 ft/min, at what rate will the boat be approaching the dock when 110 ft of rope is out?

The boat will be approaching the dock at  [answer] ft/min.

Answer 1

the rope is the hypotenuse...

y =8 is fixed

H(t) = sqrt( 64 + x^2)

dH/dt = (x) / (sqrt(x^2 + 64) dx/dt

16 = 110/ ( sqrt( 110^2 + 64)) dx/dt

16 = 110/ sqrt(12164) (dx/dt)

16*sqrt(12164)/110 = dx/dt

It's approximately 16

Answer 2