SOLUTION: A pole 12 meters long is leaning against a vertical wall of a building. If the foot of the pole is being pulled away from the wall at rate of 2 meters per minute, how fast is the t

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Question 996971: A pole 12 meters long is leaning against a vertical wall of a building. If the foot of the pole is being pulled away from the wall at rate of 2 meters per minute, how fast is the top of the pole sliding down the wall at the instant when the foot of the pole is 5 meters from the wall
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
A pole 12 meters long is leaning against a vertical wall of a building. If the foot of the pole is being pulled away from the wall at rate of 2 meters per minute, how fast is the top of the pole sliding down the wall at the instant when the foot of the pole is 5 meters from the wall
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Use x for the horizontal distance from the wall.
h = height on the wall
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h%5E2+=+12%5E2+-+x%5E2
Differentiate implicitly.
2hdh/t = -2xdx/dt
h'/x' = -x/h
At x = 5:
= -5%2Fsqrt%2812%5E2+-+5%5E2%29
= -5%2Fsqrt%28119%29 m/sec
=~ -0.458 m/sec
(Negative because it's decreasing)