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A 10​-foot ladder is leaning against a vertical wall​ when Jack begins pulling the foot of the ladder away from the wall at a rate of 0.3 ft/s.How fast is the top of the ladder sliding down the wall when the foot of the ladder is 8 ft from the​ wall?

Question
A 10​-foot ladder is leaning against a vertical wall​ when Jack begins pulling the foot of the ladder away from the wall at a rate of 0.3 ft/s.
How fast is the top of the ladder sliding down the wall when the foot of the ladder is 8 ft from the​ wall?
check_circleAnswer
Step 1

The given data can be expressed in a right triangle as shown below.

wall
L 10ft
y
ground
x 8 ft
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wall L 10ft y ground x 8 ft

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Step 2

Apply the Pythagorean theorem as follows.

x2y2
-(1)
82y10
y2 36
y6
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Image Transcriptionclose

x2y2 -(1) 82y10 y2 36 y6

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Step 3

It is given that, the rate at which the foot of the ladd...

dc
-0.3 ft/s
dt
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dc -0.3 ft/s dt

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Tagged in

Math

Calculus

Differential Equations

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