Question

A boat is pulled into a dock by means of a winch 12 feet above the deck of the boat. The winch pulls in rope at a rate of 4 feet per second. Determine the speed of the boat when there is 37 feet of rope out.
ft/sec???
can someone please tell me which formula to use???

Thanks

Answer 1

Formula? You have to think and analyze. That is the nature of physics.

In this case, you have a right triangle.

let the hypotenuse be x, the horizontal be d, and height (12).

12^2=x^2-d^2
take the derivative.
0=2x dx/dt - 2d dd/dt
or dx/dt=d/x dd/dt

but dx/dt=-4ft/sec
Next,figure d when x is 37
d^2=37^2-12^2 figure it.
dd/dt=speedboat=37/d * -4ft/s

and that is it.

Answer 2

I am still lost :(