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

calculus  ?iforget, Monday, April 6, 2015 at 4:50pm
how ambiguous a way to present the problem
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