Calculus
posted by Mehak on .
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 rightangled 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 .