Question
Asked Oct 23, 2019
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The top of a ladder slides down a vertical wall at a rate of 0.25 m/s. At the moment when the bottom of the ladder is 5 m
from the wall, it slides away from the wall at a rate of 0.6 m/s. How long is the ladder?
m
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The top of a ladder slides down a vertical wall at a rate of 0.25 m/s. At the moment when the bottom of the ladder is 5 m from the wall, it slides away from the wall at a rate of 0.6 m/s. How long is the ladder? m

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Expert Answer

Step 1

Given:

be the height up the wall to the top of the ladder.
Let x be the distance between the bottom of the wall and the bottom of the ladder
Let L be the length of the ladder
Let y
The ladder is sliding down the wall, so y is decreasing at 0.25 m/s
dy
-0.25 m/s
That is
dt
the bottom of the ladder is sliding away from the wall, so x is increasing at 0.6m/s when x=5 m.
-0.6 m/s
dt
That is
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be the height up the wall to the top of the ladder. Let x be the distance between the bottom of the wall and the bottom of the ladder Let L be the length of the ladder Let y The ladder is sliding down the wall, so y is decreasing at 0.25 m/s dy -0.25 m/s That is dt the bottom of the ladder is sliding away from the wall, so x is increasing at 0.6m/s when x=5 m. -0.6 m/s dt That is

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Step 2

Find the length of the l...

By Pythagorean theorem
dL
2L
dt
dx
dx
Diff. w.r to r
dt
2y
2x
dt
dy
dL
dx
L is constant]
+y
x
dt
dt
dt
dx
dx
-y-
dt
dt
5(0.6) y(0.25)
y 12
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By Pythagorean theorem dL 2L dt dx dx Diff. w.r to r dt 2y 2x dt dy dL dx L is constant] +y x dt dt dt dx dx -y- dt dt 5(0.6) y(0.25) y 12

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