The top of a ladder slides down a vertical wall at a rate of 0.5m/s. at the moment when the bottom of the ladder is 3m from the wall, it slides away from the wall at a rate of 0.2m/s. how long is the ladder?

The length of the ladder is 3.23 m

Explanation:

Let's call the distance from the top of the ladder to the ground, the distance from the bottom of the ladder to the wall and the the length of the ladder.

So, we can write the following equation:

So, if we derive both sides of the equation with respect to t, we get:

Solving for y, and replacing the values of x by 3, by 0.2m/s and by -0.5m/s, we get:

Then, if is equal to 3 m and is equal to 1.2m, is equal to:

this could be newton#'s law of cooling. the cooling curve is exponential