Question

A boat is held at a dock by a bow line which is wound about a circular windlass 3 feet higher than the bow of the boat. How fast is the bow line increasing its length at the instant the boat is 4 feet from the dock if the boat is drifting at a rate of 7 feet per second from the dock?

Answer 1

let the length of line be L ft
let the horizontal distance of the boat from the dock be x ft

You have a right-angled triangle, thus

x^2 + 3^2 = L^2
2x dx/dt = 2L dL/dt
for the given case: x = 4
L^2 = 4^2 + 3^2
L = 5

2(4)(7) = 2L dL/dt
dL/dt = 2(5)/(56) = 5/28 ft/s

Answer 2

Hi,
Thank you but why are we plugging in the 4 afterwards when it is already given so why don'y we just use it in the beginning?

Answer 3

Oh nevermind I think its because the initial x isn't given and they want us to find the x when it is 4 feet away right?