Calculus
posted by saud on .
A 15 ft ladder leans against a wall. The bottom of the ladder is 4 ft from the wall at time t=0 and slides away from the wall at a rate of 3ft/sec.
Find the velocity of the top of the ladder at time t=2.
The velocity of ladder at time t=2 is ........ft/sec.

let foot of ladder be x ft from wall
let top of ladder by y ft above grouns
x^2 + y^2 = 15^2
2x dx/dt + 2y dy/dt = 0
so when t = 2, x = 4+6 = 10
y^2 = 225100 = 125
y = √125 , and dx/dt = 3
2(10)(3) + 2(√125 dy/dt = 0
dy/dt = 60/(2√125)
= 30/√125
= appr. .2.68 ft/sec
(the negative sign indicates the ladder is moving downwards) 
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