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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?
Asked by Reena Last Modified
Answer 
Harshit Bhardwaj
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
.
Related Questions
The rate of change of the area of a circle with respect to its radius r at r = 6 cm is
(A) 10π (B) 12π (C) 8π (D) 11π
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