The Progression-Mathematics Problem

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Suppose that there is a rubber ball which has a property of bouncing back to the original height from which it was dropped and it keeps doing that until it is stopped by any external force.

Can you calculate the fraction of height to which the ball would have bounced if it has bounced four times after dropping from a certain height without being stopped?

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    16/81

    Explanation:
    It is a question of geometric progression but we can solve it step by step as well in case you are not aware of the formula.

    At first bounce
    The height at which the ball would have reached = 2/3 of the original height from which it was dropped.

    At second bounce
    The height at which the ball would have reached = 2/3 * 2/3 of the original height from which it was dropped.

    At third bounce
    The height at which the ball would have reached = 2/3 * 2/3 * 2/3 of the original height from which it was dropped.

    At fourth bounce
    The height at which the ball would have reached = 2/3 * 2/3 * 2/3 * 2/3 of the original height from which it was dropped.

    Now, 2/3 * 2/3 * 2/3 * 2/3 = 16/81

    Therefore, 16/81 of the original height from which the ball was dropped is the required fraction height.

    ronret45 Expert Answered on 8th August 2015.

    how they are saying It bouncing the same height from where it drouped

    on 19th January 2016.
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