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 = 225-100 = 125
y = √125 , and dx/dt = 3
2(10)(3) + 2(√125 dy/dt = 0
dy/dt = -60/(2√125)
= appr. -.2.68 ft/sec
(the negative sign indicates the ladder is moving downwards)
according to the ap wizardry handbook, using the demon spawn spell, the problem can be obliterated thorugh fire spitting dragons that originiate from the vave of JF.