A ladder 5 m long is leaning against a wall. The bottom of the ladder is pulled along the ground, away from the wall, at the rate of 2cm/s. How fast is its height on the wall decreasing when the foot of the ladder is 4 m away from the wall?

Question

Philoid · Accepted Answer

Let y be the height of the wall at which the ladder touches. Also, let the foot of the ladder be x m away from wall.

we know that, by Pythagoras theorem,

x² + y² = 25

Then, the rate of change of height (y) with respect to time (t) is given by:

Now, it is given that

Therefore,

And when x= 4m, then

=

Therefore, the height of the ladder on the wall is decreasing at the rate of cm/s.