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A 2 m ladder leans against a vertical wa...

A `2 m` ladder leans against a vertical wall. If the top of the ladder begins to slide down the wall at the rate `25cm//sec.`, then the rate `("in cm"//"sec".)` at which the bottom of the ladder slides away from the wall on the horizontal ground when the top of the ladder is `1 m` above the ground is :

A

`(25)/(sqrt3)`

B

25

C

`25sqrt3`

D

`(25)/(3)`

Text Solution

Verified by Experts

The correct Answer is:
A
`x^(2)+y^(2)=4`
`(dx)/(dt)+(2ydy)/(dt)=0`

`(dy)/(dt)=(-(xdx)/(dt))/(u)=-(1(25))/(sqrt3)=-(25)/(sqrt3)" cm/sec"`
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