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A ladder 10 m long rests against a verti...

A ladder 10 m long rests against a vertical wall with the lower end on the horizontal ground. The lower end of the ladder is pulled along the ground away from the wall at the rate of 3 m/s. The height of the upper end while it is descending at the rate of 4 m/s, is

A

`4sqrt(3)` m

B

`5sqrt(3)` m

C

`5sqrt(2)` m

D

6 m

Text Solution

Verified by Experts

The correct Answer is:
D
Let AB = x m, BC = y m
and AC = 10 m
`:." "x^(2)+y^(2)=100" "...(i)`
`implies" "2x(dx)/(dt)+2y(dy)/(dt)=0`
`implies" "2x(3)-2y(4)=0`
`["Given",(dx)/(dy)=3m//s,(dy)/(dt)=-4m//s]`

On putting this value in Eq. (i), we get
`(16)/(9)y^(2)+y^(2)=100`
`implies" "y=6" m"`
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