Posted by **sam** on Wednesday, September 29, 2010 at 2:48pm.

A boat is pulled into a dock by a string attached to the bow of the boat and passing through a pulley on the dock that is1ft higher than the bow of the boat. If the string is pulled at a rate of 3 ft/second, how fast is the boat approaching the dock when it is 7 ft from the dock?

- calculus -
**Reiny**, Wednesday, September 29, 2010 at 4:55pm
Make a diagram, you should have a right-angled triangle.

let the horizontal distance of the boat from the dock be x ft

let the hypotenuse, the length of the rope, be y ft.

then x^2 + 1^2 = y^2

2xdx/dt = 2ydy/dt

when x=7

y^2 = 7^2 + 1^ = 50

y = √50

and you are given dy/dt = -3 ft/s (I made it negative since y is decreasing)

sub in and you are on your way.

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