Question

A man on a wharf is pulling in a boat by means of a rope attached to the bow of the boat 1 meter above water level and passing through a simple pulley located on the dock 8 meters above water level. If he pulls in the rope at the rate of 2 meters per second, how fast is the boat approaching the wharf when the bow of the boat is 25 meters from a point that is directly below the pulley?

Answer 1

h height above bow (constant=7)
y hor distance to bow (25 at moment)
x = our rope length
x^2 = h^2 + y^2
2 x dx = 0 + 2ydy
dy/dx = x/y
dy/dt = dy/dx dx/dt = 2 (x/y)

x = sqrt (7^2 + 25^2) = 26
so
dy/dt = 2 (26/25) = 2.08 m/s