A body falls 8m in the 1^st second of the motion, 24 meters in the 2^nd,40 meters in the 3^rd and so on.How long will it take to fall 2048 meters?

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Solution

Given, the boy falls 8 m in 1st second, 24 m in the 2nd second, 40 m in the 3rd second ...

8m, 24m , 40 m, ... are in A.P.

Here a = 8 m and d = 24 m – 8 m = 16 m

Suppose the boy takes n seconds to fall 2048 m.

In each second it falls 16 metres further than in the previous second. In the nth second it falls 16n - 8 metres.
So after n seconds it has fallen 8 + 24 + 40 + ... + (16n - 8) metres
The sum of the first n terms of an arithemetic sequence is (n/2) times the sum of of the 1st and nth terms, i.e.:
S = (n/2)(8 + (16n - 8))
S = (n/2)(8 + 16n - 8)
S = (n/2)(16n)
S = 8n^2
Therefore:
8n^2 = 2048
n^2 = 2048/8
n^2 = 256
n = sqrt(256)
n = 16

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A body falls 8m in the 1st second of the motion, 24 meters in the 2nd ,40 meters in the 3rd and so on.How long will it take to fall 2048 meters?

A body falls 8m in the 1^st second of the motion, 24 meters in the 2^nd,40 meters in the 3^rd and so on.How long will it take to fall 2048 meters?