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A ladder, 5 maters long, standing on a h...

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

A

`10 m//s`

B

`3/2 m//s`

C

`8/3 m//s`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
C
At any instant `x^(2)+y^(2)=5^(2)`
Differentiating w.r.t. time `2x x/(dt)+2y (dy)/(dt)=0`
Here `(dx)/(dt)=2, (dy)/(dt)=u rArr u=8/3 m//s`
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Knowledge Check

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

    A
    `(1)/(10)` radian/sec
    B
    `(1)/(20)` radina/sec
    C
    5 radian/sec
    D
    10 radian/ sec

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