Homework Help: Calculus

Posted by bryan on Sunday, February 3, 2013 at 12:28pm.

A boat is pulled into a dock by a rope attached to the bow of the boat and passing through a pulley on the dock that is 1 m higher than the bow of the boat. If the rope is pulled in at a rate of 1 m/s, how fast is the boat approaching the dock when it is 8 m from the dock?

Calculus - Steve, Sunday, February 3, 2013 at 2:30pm
If the rope is of length h, and the boat is x away from the dock,

h^2 = 1+x^2
When x=8, h = √65

2h dh/dt = 3x dx/dt
Since dh/dt = -1,

2√65 (-1) = 3*8 dx/dt
dx/dt = -√65/12

Since dx/dt < 0, the boat is approaching the dock at about 0.67 m/s

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