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

Options

A. `4sqrt(3)m`
B. `5sqrt(3)m`
C. `5sqrt(2)m`
D. `6m`

Answer

D

Explanation

Let `AB=xm, BC=ym` and `AC=10m`
`:.x^(2)+y^(2)=100`…………….i

`implies2x(dx)/(dt)+2y(dy)/(dt)=0`
`implies 2x(3)-2y(4)=0`
`[ :' (dx)/(dt)=3, (dy)/(dt)=-4` given `]`
`implies x=(4y)/3`
On putting this value is eq i we get
`16/9y^(2)+y^(2)=100impliesy^(2)=(100xx9)/25=36`
`implies y=6m`