Question

# A boat is pulled into a dock by a rope attached to the bow of the boat an passing through the pulley on the deck that is 1m high than the bow of the boat ,if the rope is pulled im at the rate of 0.8m/s how fast does the boat approach the deck when it is 1

A boat is pulled into a dock by a rope attached to the bow of the boat an passing through the pulley on the deck that is 1m high than the bow of the boat ,if the rope is pulled im at the rate of 0.8m/s how fast does the boat approach the deck when it is 10m from the dock?

I hope you made a diagram.

Let the distance of the boat to the dock be x m
let the length of the rope be y m

given: dy/dt = -.8 m/s
find dx/dt when x = 10

you will have the right-angled triangle such that
x^2 + 1 = y^2
2x dx/dt = 2y dy/dt
dx/dt = y/x (dy/dt)

when x=10
y^2 = 101
y = √101

dx/dt = √101/10(-.8) = -.804

the distance is decreasing at a rate of .804 m/second
Yea i did made a diagraam and thanks .

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