Question

A ladder , 5 meter long , standing on a horizontal floor , leans against a vertical wall . If the top of the ladder slides downwards at the rate of 10 cm/sec . Find the rate at which the angle between the floor and the ladder is decreasing when the lower end of the ladder is 2 meter from the wall .

Answer 1

let the ladder reach h m high on the wall, let the base angle be Ø
sinØ = h/5
h = 5sinØ
dh/dt = 5cosØ dØ/dt

given: dh/dt = -10m/sec
when base = 2m, cosØ = 2/5

-10 = 5(2/5) dØ/dt
dØ/dt = -5 radians/sec

the angle is decreasing at a rate of 5 radians / sec

(by using the word "decreasing" I do not include the negative sign)

Answer 2

Change first 5m to 500cm and 2m to 200cm and then solve using above procedure of reiny answer is 1/20 radians/sec