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Question

A ladder, 5 meter long, standing on a horizontal floor, leans against vertical wall. If the top of the ladder slides downwards at the rate of 10cm/sec, then the rate at which the angle between the floor and the ladder is decreasing when lower end of ladder is 2 metres from the wall is:

A
110radian/sec
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B
120radian/sec
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C
20radian/sec
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D
10radian/sec
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Solution

The correct option is B 120radian/sec
The required problem be,
Let, angle between floor and the ladder be θ
Let at any time t AB=xcm and BC=ycm
So,
sinθ=x500 and ,
cosθ=y500
or, x=500sinθ
or, y=500cosθ
Also given that
dxdt=10cm/s
implies that,
500.cosθ.dθdt=10
implies that,
dθdt=150cosθ
dθdt=150.y500

=10y

=10200

Hence the requires angle is

=120rad/s


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