A ladder 5 m long is leaning against a wall The bottom of the ladder is pulled along the - Maths - Application of Derivatives

Question

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 2 cm/s How fast is its height on the wall decreasing when the
foot of the ladder is 4 m away from the wall?

Gopal Mohanty · Accepted Answer

Let y m be the height of the wall at which the ladder touches Also, let the foot of the ladder be x maway from the wall Then, by Pythagoras theorem, we have: x2 + y2 = 25 [Length of the ladder = 5 m]

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

It is given that

Now, when x = 4 m, we have:

Hence, the height of the ladder on the wall is decreasing at the rate of

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 2 cm/s. How fast is its height on the wall decreasing when the foot of the ladder is 4 m away from the wall?