A ladder 10 ft long rests against a vertical wall.

Question

If the bottom of the ladder slides away from the wall at a rate of 1.2 ft/s, how fast is the angle between the ladder and the ground changing when the bottom of the ladder is 8 ft from the wall?

Answer 1

Answer 2

cosθ = x/l; sinθdθ/dt = (dx/dt)/l; dθ/dt = (dx/dt)/(lsinθ) = (dx/dt)/√(l² - x²) = 1.2ft/s/6ft = 0.2 rad/s