Question

A ladder is 10 m long rests against a vertical wall with the lower end on the horizontal ground. The lower end of the ladder is pulled along the ground away from the wall at the rate of 3 cm/s. The height of the upper end while it is descending at the rate of 4 cm/s is ______.

पर्याय

• `4sqrt(3)` m

• `5sqrt(3)` m

• 8 m

• 6 m

Answer 1

A ladder is 10 m long rests against a vertical wall with the lower end on the horizontal ground. The lower end of the ladder is pulled along the ground away from the wall at the rate of 3 cm/s. The height of the upper end while it is descending at the rate of 4 cm/s is 6 m.

Explanation:

Let AB = x m, BC = y m and AC = 10 m

∴  x² + y² = 100   ...(i)

`2x  dx/dt + 2y dy/dt` = 0

So, 2x (3) – 2y (4) = 0

Given, `dx/dt` = 3 m/s, `dy/dt` = – 4 m/s

`\implies` x = 4y / 3

Putting this value in equation (i), we get

`16/9 y^2 + y^2` = 100

`\implies` 16y² + 9y² = 900

`\implies` 25y² = 900

`\implies` y = 30 / 5 = 6 m