Question
Asked Dec 3, 2019
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The top of a ladder slides down a vertical wall at a rate of 0.15 m/s. At the moment when the bottom of the ladder is 3 m from the wall, it slides away from the wall at a rate of 0.2 m/s. How long is the ladder?

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Expert Answer

Step 1

Given,

A
0.15m/s
A'
Ladder
Wall
В
C 0.2 m/s
с
ВС - 3m
d
(AB) = -0.15m/s negative sign due to downwards]
dt
d
(BC) 0.2 m/s
dt
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A 0.15m/s A' Ladder Wall В C 0.2 m/s с ВС - 3m d (AB) = -0.15m/s negative sign due to downwards] dt d (BC) 0.2 m/s dt

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Step 2

According to Pythagoreans theorem,

AC2 AB2BC
...1)
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AC2 AB2BC ...1)

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Step 3

Differentiate equation (1) with r...

d
-AC (AB+BC
dt
dt
d
d
d
2АС (АС)-2АВ " (АВ)+ 2BС- (ВC)
dt
dt
dt
d
(AC) 0, AC is the length of ladder
dt
d
AC (0) AB-
dt
(АВ)+ ВС (ВС)
dt
which not change with time.
...2)
- (АB) + ВС(ВС)
dt
0= AB
dt
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d -AC (AB+BC dt dt d d d 2АС (АС)-2АВ " (АВ)+ 2BС- (ВC) dt dt dt d (AC) 0, AC is the length of ladder dt d AC (0) AB- dt (АВ)+ ВС (ВС) dt which not change with time. ...2) - (АB) + ВС(ВС) dt 0= AB dt

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