Question

A ladder 10 ft long rests against a vertical wall. If the bottom of the ladder slides away from the wall at a rate of 2 ft/s, how fast is the angle between the ladder and the ground changing when the bottom of the ladder is 5 ft from the wall? Evaluate your answer numerically. (Round the answer to three decimal places.)

Answer 1

let x be the horizontal distance from wall to ladder.

cosineTheta=x/10

10 cosTheta=x

-10sinTheta dTheta/dt= dx/dt

so you are looking for dTheta/dt

when x=5, theta = arccos.5, or 60 deg, and sin of 50 = .877

dTheta/dt= dx/dt / (10*.877)

check all that.

Answer 2

.228