A boat is being pulled into a dock at a constant rate of 30ft/min by a winch located 10ft above the deck of the boat.

10^2 + x^2 = y^2

derivative 2x * dx/dt = 2y * dy/dt

  1. 50 feet out?

x=50

102+x2=y^2

y2=102+50^2

y^2=100+2500

y=50.99

50 * dx/dt= 50.99 * 30

dx/dt = 30.59

  1. 15 feet out?

x=15

102+x2=y^2

y2=102+15^2

y^2=100+225

y=18.02

15 * dx/dt=18.02 * 30

dx/dt=36.04

  1. 1 foot from the dock ?

x=1

102+x2=y^2

y2=102+1^2

y^2=100+1

y=10.05

1 * dx/dt= 10.05* 30

dx/dt=301.50

  1. What happens when the length of rope pulling in the boat is less than 10 feet long?

It takes less than a minute to pull back to the dock.