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 ts height on the wall decreasing, when the foot of the ladder is 4 m away from the wall ?

Answer 1

Let AB be the ladder and OB be the wall.

At any instant, let OA = x m and OB = y m.

Also AB = 5 M,

. ^.. x² + y² = 5² = 25

Differentiating (i) w.r.t. 't', we get

Thus, the height of the Iadder on the wall is decreasing at the rate of 8/3 cm/sec.