A ladder 5 m in length is leaning against a wall. The bottom of the ladder is pulled along the ground away from the wall, at the rate of 2 ~m / sec . How fast is the height on the wall decreasing when the foot of the ladder is 4 m away from the wall?

Step-by-step solution

In right angled AOC , aligned & x^2+y^2=(5)^2 & y^2=5^2-x^2 aligned Differentiating w.r.t. t, we get aligned 2 y ~d y dt & =-2 x ~d x dt d y dt & =- x y ~d x dt & = -x 5^2-x^2 ~d x dt aligned aligned ( d y dt )_ x=4 & = -4 25-16 (2) & = -8 3 ~m / sec aligned Thus; the height on the wall is decreasing at the rate of 8 3 ~m / sec