Question

A particle is dropped from a certain height. The time taken by it to fall through successive distances of 1km each will be in the ratio of.....??

Answer 1

Answer:

Explanation:

Given A particle is dropped from a certain height. The time taken by it to fall through successive distances of 1 km each will be in the ratio of

 We know that time taken to travel distance s using equation of motion is

 S = ut + 1/2 gt^2

 S = 0 + 1/2 gt^2

 So t = (2S / g)^1/2

Let it travel 1 m in time t1

So t1 = (2/g)^1/2

If it travels 2 m in time t

Then t = (4/g)^1/2

So it travels the next 1 m in t2 = t – t1

                                                = (4/g)^1/2 – (2/g)^1/2

                                             t2 = (2/g)^1/2 (√2 – 1)

Suppose it travels 3 m in time t’

t’ = (6/g)^1/2

Therefore it travels the next 1 m in time t3 = t’ – t

                                                  t3 = (6/g)^1/2 – (4/g)^1/2

                                                 t3 = (2/g)^1/2 [√3 - √2

Thus

 T1 : t2 : t3 = 1 : [√2 – 1] : [√3 - √2]

Answer 2

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