Question

Aball is dropped from 8m and it rises half of its previous height when a ball hits the ground for the seventh time how far had it traveled?

Answer 1

Solution :

Here , it is given that , if a ball is dropped from a certain height of 8m, it rises to half its height and so on .

Let us assume that it is initially dropped from a height of h m .

The number of times it is repeatedly hit be n .

So, the height it rises the n+1 th time :

> $\frac{1}{2^{(n+1)}} h$

Now, it is given that it hits the ground for the 7th time.

So,

The height it rises the 8th time :

> 1/2^8 * h

Total distance travelled :

> h + (1/2) h + ....................... + (1/2^8) h

> h [ 1 + 1/2 + 1/4 + ............. + 1/2^8]

Sum of gp series :

> 2h

> 16 m.

This is the required answer.

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