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
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Use x for the horizontal distance from the wall.
h = height on the wall
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{{{h^2 = 12^2 - x^2}}}
Differentiate implicitly.
2hdh/t = -2xdx/dt
h'/x' = -x/h
At x = 5:
= {{{-5/sqrt(12^2 - 5^2)}}}
= {{{-5/sqrt(119)}}} m/sec
=~ -0.458 m/sec
(Negative because it's decreasing)