Posted by **skullhong** on Thursday, March 22, 2012 at 8:23am.

A ladder 10 meter long is leaning against a wall. If the top of the ladder is sliding down the wall at 3m/s, how fast is the angle between the top of the ladder and the wall changing when the foot of the ladder is 6 meter away from the wall?

- mathematic -
**Reiny**, Thursday, March 22, 2012 at 10:02am
let the angle you mentioned be Ų

Let the foot of the ladder be x ft from the wall, and the height of the ladder be y ft

cosŲ = y/10

y = 10cosŲ

dy/dt = -10sinŲ dŲ/dt

when x = 6

x^2+y^2=100

y = 8 , and sinŲ = 8/10

Also we know dy/dt = -3 m/s

-3 = -10(8/10)(dŲ/dt)

dŲ/dt = 3/8 radians/s

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