Posted by **Arvin** on Wednesday, October 17, 2012 at 7:34am.

A ladder 10 ft 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 20 degrees with the ground.

- Calculus -
**Reiny**, Wednesday, October 17, 2012 at 9:31am
let the top of the ladder by y ft up on the wall

let the angle made at the foot be Ų

sinŲ = y/10

10 sinŲ = y

10 cosŲ dŲ/dt = dy/dt

given: when Ų = 20° , dy/dt = -5 ( y is decreasing)

10 cos20° dŲ/dt = -5

dŲ/dt = -1/(2cos20°) = -.532 radians/sec

or angle is decreasing at .532 radians / sec

which is appr. 30.5° / sec

(notice the angle is changing very rapidly at that moment, since the ladder has almost fallen)

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