Question

The top of a ladder slides down a vertical wall at a rate of 0.675 m/s . At the moment when the bottom of the ladder is 3 m from the wall, it slides away from the wall at a rate of 0.9 m/s . How long is the ladder

Answer 1

L = 5 m

Explanation:

The ladder, the vertical wall and the ground form a right triangle. We call A and B the ends points of the ladder ( at the wall, and the ground)

If we call L the lenght of the leadder, we get

L² = y² + x²

Taking derivatives on both sides of the equation

0 = 2y Dy/dt + 2x Dx/dt

We know that Dy/dt = - 0,675 m/s (is sliding down , is decreasing)

And when x = 3 m Dx/dt = 0,9 m/s

So we can get y

0 = 2y*( -0,675) + 2*3*0,9

1,35y = 5,4

y = 5.4 /1,35 ⇒ y = 4

And L² = y² + x² ⇒ L = √ (4)² + (3)² ⇒ L √16 + 9

L = 5 m