# Thread: Rate of change question

1. ## Rate of change question

A ladder 5m long leans against a vertical wall. The bottom of the ladder is pulled along the ground away from the wall at a constant rate of 0.5 m/s.

How fast will the top of the ladder be falling at the instant it is 2m above the ground?

Can anyone guide me. Thank you.

2. ## Re: Rate of change question

Originally Posted by MichaelLight
A ladder 5m long leans against a vertical wall. The bottom of the ladder is pulled along the ground away from the wall at a constant rate of 0.5 m/s.

How fast will the top of the ladder be falling at the instant it is 2m above the ground?

Can anyone guide me. Thank you.
If $\displaystyle y$ denotes the height at which the ladder touches the wall and $\displaystyle x$ the distance of the foot of the ladder is from the wall then by Pythagoras's theorem:

$\displaystyle x^2+y^2=5^2$

You are being asked to find $\displaystyle dy/dt$ when $\displaystyle y=2$ and you are told that $\displaystyle dx/dt=0.5$ (distances in metres and times in seconds).

CB