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?

Options

A. `10 m//s`
B. `3/2 m//s`
C. `8/3 m//s`
D. None of these

Answer

C

Explanation

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`