Homework Help: calculus

Posted by Anonymous on Wednesday, October 10, 2012 at 10:20pm.

a man on a dock is pulling in a boat by means of a rope attached to the bow of the boat 1ft above the water level and passing through a simple pulley located on a dock 8ft above the water level. if he pulls in the rope at a rate of 2ft/sec, how fast is the boat approaching the dock when the bow of the boat is 24ft from the point that is directly below the pulley?

calculus - Steve, Thursday, October 11, 2012 at 10:37am
consider y=0 at the bot bow, so the pulley is at height 7

if the boat is at distance x, the length r of the rope from pulley to boat, is given by

r^2 = x^2 + 7^2
when x=24, r=25
dr/dt = -2

2r dr/dt = 2x dx/dt
2(25)(-2) = 2(24) dx/dt

dx/dt = -25/12 ft/s

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