Question

A 13ft ladder is leaning against a wall when its base starts ti slide away from the wall. By the time its base is 12 feet from the wall, the base is moving at the rate of 5ft/sec. How fast is the top of the ladder sliding down the wall?

Answer 1

Given :

A 13ft ladder is leaning against a wall when its base starts ti slide away from the wall.

By the time its base is 12 feet from the wall, the base is moving at the rate of 5ft/sec.

To Find :

How fast is the top of the ladder sliding down the wall.

Solution :

By, Pythagoras theorem, distance of ladder from horizontal to wall is 5 feet.

Now,
`x^2 + y^2 = 13^2`

Differentiating both sides, we get :

`2x(dx)/(dt)+2y(dy)/(dt)=0\\\\(2* 12* 5) + (2* 5 * (dy)/(dt))=0\\\\(dy)/(dt)= -12 \ feet/sec`