Q. 10 4.1( 72 Votes )

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?

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 the 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


And when x= 4 m, then


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

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