A boat is pulled into a wharf by a rope at a speed of 20m/min. If the rope is attached to a point on the boat 7m vertically below the wharf, at what rate is the rope being drawn in when the boat is 24m from the wharf?

Answer 1

When the boat is x meters from the wharf, the length r of rope is

r^2 = 7^2 + x^2
r dr/dt = x dx/dt
Now plug in your numbers and solve for dr/dt

I find this a bit odd, since I'd think that dr/dt would be constant. Instead, somehow the boat's speed is being kept constant.

Oh, well.