SOLUTION: A boat is being pulled toward a dock by means of a cable attached to a windlass 9 feet above the deck of the boat. The cable is being wound in at a rate of 6 feet per second. How f

Question 857260: A boat is being pulled toward a dock by means of a cable attached to a windlass 9 feet above the deck of the boat. The cable is being wound in at a rate of 6 feet per second. How fast is the boat approaching the dock when its horizontal distance to the dock is 12 feet?
I don't even know how to start this problem, so thank you for your help!
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
You have to do a sketch of this
( if you haven't already )
In order to understand it. Show the surface
of the water and the boat 12 ft from the dock
Show a point where the windlass is on the
dock 9 ft above the surface of the water.
-------------------------------------------
Draw the cable that connects the windlass to the boat.
Now draw an arrow along this line representing
the velocity of the cable as it pulls the boat
( from the boat towards the windlass )
-------------------------------------------------
Now show horizontal and vertical components
of this velocity. One component is straight up
and the other component is horizontal. It is only
this horizontal component which contributes
velocity which moves the boat closer to the dock.
The vertical component contributes nothing.
--------------------------------------------------
The cable forms a 9 - 12 - c right triangle. Find c.

-----------------
This is the length of the cable, and the velocity is
also along this line. I want to find the horizontal
component, x, of the velocity. I can say:

when the boat's horizontal distance to the dock is 12 feet,
It is approaching the dock at a rate of 3.6 ft/sec.
Hope it's not confusing.

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