Question

A boat pulls away from a dock at 2 m/s, but the operator has neglected to remove the tow rope used to pull the boat up to the dock. This rope runs thru a pulley which is attached to the dock at a point 1 m higher than the point at which the rope is attached to the boat.

A) How fast is the rope being pulled out when the boat is 3 m away from the dock

B) How fast is the rope is pulled as the distance from the dock grows large? Justify your answer

Answer 1

at a distance x, the length of rope (z) is

z^2 = x^2+1

now just find dz/dx at x=3

it should be clear how z changes when x is large.

Answer 2

oops. I meant find dz/dt.