Question

A ladder 20 ft Jong leans against a vertical wall. The top-end slides downwards at the rate of 2 ft per second. The rate at which the lower end moves on a horizontal floor when it is 12 ft from the wall is ______ 

Options

• `8/3`

• `6/5`

• `3/2`

• `17/4`

Answer 1

A ladder 20 ft Jong leans against a vertical wall. The top-end slides downwards at the rate of 2 ft per second. The rate at which the lower end moves on a horizontal floor when it is 12 ft from the wall is `underline(8/3)`.

Explanation:

 

According to the figure, x² + y² = 400 .........(i)

Differentiate (i) w.r.t. t, we get

`2xdx/dt + 2ydy/dt = 0` ...................(ii)

Here x = 12 and `dy/dt = 2`

From (i), 12² + y² = 400

⇒ y = 16

From (ii), 2(12) `dx/dt + 2(16)(2) = 0`

⇒ `dx/dt = 8/3`