Question

Choose the correct option from the given alternatives :

A ladder 5 m in length is resting against vertical wall. The bottom of the ladder is pulled along the ground away from the wall at the rate of `(1.5 "m")/sec`. The length of the higher point of ladder when the foot of the ladder is 4.0 m away from the wall decreases at the rate of

पर्याय

• 1

• 2

• 2.5

• 3

Answer 1

2

Explanation:

Given L = 5 m, `dx/dt = (1.5 "m")/sec` and x = 4

using pythagoras theorem,

x² + y² = L²     ...(1)

differentiating both sides w.r.t

`2xdx/dt + 2y dy/dt = 0`

`dy/dt = -x/y dx/dt`

at x = 4,

y = `sqrt("L"^2 - x^2)` 

= `sqrt(5^2 - 4^2)` 

= 3m.

∴ `dy/dt = -4/3 xx 1.5`

= `(-4)/3xx3/2`

= - 2 m/sec

Hence, it Decreases at the rate of 2m/sec.

∴  So, 2m/sec is correct answer.