Question

a ladder of 10 ft long leans against a vertical wall. the upper end slips down the wall at 5 ft/sec. how fast is the ladder turning when it takes an angle of 30 degree with the ground?

Answer 1

if the ladder reaches up h feet,

sinθ = h/10

cosθ dθ/dt = 1/10 dh/dt

You know θ and dh/dt, so solve for dθ/dt.

Answer 2

dθ/dt = sqrt(3)/3