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A ladder 5m long is leaning against a wa...

A ladder 5m long is leaning against a wall. The foot of the ladder is pulled out along the ground away from from the wall at a rate of `2 m//s`. How fast is the height of ladder on the decreasing at the instant when the foot of the ladder is `4 m` 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 13 m long is leaning against a wall. The bottom of the ladder is pulled along the ground away from the wall at the rate of 4 m/sec. Find the rate of decreasing at which the top of the ladder moving downwards on wall when the foot of the ladder is 5 m away from the wall.

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