SOLUTION: please help me solve this question:a rubber ball is dropped from a height of 10 meters,suppose it rebounds half the distance after each fall,find the total distance the ball travel

Question 1111661: please help me solve this question:a rubber ball is dropped from a height of 10 meters,suppose it rebounds half the distance after each fall,find the total distance the ball travels.
thank you
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
The first bounce(s1) it covers 10+(10/2) = 15m.
:
The second bounce(s2), it is (10/2)+(10/4) = 7.5m
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The third bounce(s3), it is (10/4)+(10/8) = 3.75m and so forth
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The distance covered by each bounce is 1/2 the distance covered by the previous bounce
:
The total distance covered is the sum of the partial sums,
:
total distance = s1 + s2 + s3 + ...... + sn
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Note that the partial sums si form a geometric series where the common ratio is 1/2
:
si = s1 * (1/2)^(n-1), where i = 1, n
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when the absolute value of the common ratio is less than 1, the sum is defined as
:
sum = s1 / (1 - r), where s1 is the initial term and r is the common ratio
:
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sum = 15 / (1 - (1/2)) = 15 * 2 = 30m
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