Question

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.

Answer 1

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)
= -30/√125
= appr. -.2.68 ft/sec

(the negative sign indicates the ladder is moving downwards)

Answer 2

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.