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Sliding Ladder (Posted on 2024-07-31)

A ladder 20 ft long is leaning against a wall. Now, the bottom of the ladder is pushed horizontally away from the wall at a rate of 1.5 ft/sec.

How fast is the top of the ladder sliding down the wall when the bottom is 16 ft from the wall?

No Solution Yet Submitted by K Sengupta

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Solution

Comment 1 of 1

x^2 + y^2 = 400

y = √(400 - x^2)

dx/dt = 1.5 ft/sec (call it positive because x is increasing)

dy/dt = -(2x)(dx/dt) / 2√(400 - x^2)

dy/dt at x=16 is

-(16)(1.5) / √(400 - 256)

- 24 / √144 = -2 ft/sec

Posted by Larry on 2024-07-31 09:53:50

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