Question

a particle is dropped from certain height the time taken by it to fall through successive distance of 1m each will be​

Answer 1

Answer:

Explanation:

a particle is dropped from certain height the time taken by it to fall through successive distance of 1m each will be​

particle is dropped =>u = 0

a = g

S = ut + (1/2)gt²

=> S = (1/2)gt²

=> t² = 2S/g

=> t = √ 2S/g

for S = 1

t₁ = √ 2/g

for Next 1 meter ( 1 to 2 m)

t₂ - t₁ = √ 2*2/g - √ 2/g = √ 2/g (√ 2 - 1)

for further Next 1 meter (2 to 3 m)

t₃ - t₂ = √ 2*3/g - √ 2*2/g = √ 2/g (√ 3 - √ 2)

for further Next 1 meter (3 to 3 4)

t₃ - t₂ = √ 2*4/g - √ 2*3/g = √ 2/g (√ 4 - √ 3)

for nth meter

tn - t(n-1) =

√ 2/g = √ 2/g (√ n - √ n-1)

√ 2/g  ,  √ 2/g (√ 2 - 1) , √ 2/g (√ 3 - √ 2) , √ 2/g (√ 4 - √ 3) .......√ 2/g (√ n - √ n-1)

Ratio

1 : √ 2 - 1 : √ 3 - √ 2 : √ 4 - √ 3 : .................. :√ n - √ n-1