Question

if an object takes 40 seconds to fall from 1000 meters height , find the time taken by it to fall from 750 meters height ? ​

Answer 1

Given info : an object takes 40 seconds to fall from 1000 m height.

To find : the time taken by it to fall from 750 m height is...

solution : when a object starts falling, initial velocity of object , u = 0

let acceleration is a

object is falling from a tower of height h.

using formula, s = ut + 1/2 at²

here, s = h , u = 0

so, h = 1/2 at²

⇒t = √(2h/a)

here it is clear that time taken by an object to fall the ground is directly proportional to square root of height of object.

i.e., t₁/t₂ = √(h₁/h₂)

here t₁ = 40 s , t₂ = ?, h₁ = 1000 m , h₂ = 750 m

so, 40/t₂ = √(1000/750) = √(4/3)

⇒t₂ = 40/√(4/3) = 20√3 = 20 × 1.732 = 34.64 s

Therefore time taken to fall from 750 m height is 34.64 m.