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. `6m`
D. 8 m

Answer

C

Explanation

Let AB=x metre, BC=y metre

and AC=10 cm
`thereforex^(2)+y^(2)=100`
On differentiating w.r.t. t, we get
`2x(dx)/(dt)+2y(dy)/(dt)=0`
`implies2x(3)-2y(4)=0`
`impliesx=(4y)/(3)`
On putting the value of X value in Eq. (i) we get
`(16)/(9)y^(2)+y^(2)=100` ,brgt `impliesy^(2)=(100xx9)/(25)=36`
`impliesy=6m`