Draw a diagram. If the boat is x meters from the pier, the rope haas length r, with
r^2 = x^2+1
So,
2r dr/dt = 2x dx/dt
when x=5, r=√26, so
2√26(-1) = 2(5) dx/dt
dx/dt = -√26/5
so, the boat is approaching the dock at about 1.0 m/s
Makes sense, since x and r are almost the same for x relatively large compared to 1.
A pulley system on a pier is used to pull boats towards the pier for docking. Suppose that a boat is being docked and has a rope attaching the boat's bow on one end and feeding through the pier's pulley system on the other end. The pulley system is 1 meter higher than the height of the boat's bow. The rope is being pulled in at a rate of 1 m/s. When the boat is 5 meters from the pier, how fast is the boat approaching the pier?
1 answer
1 answer