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Maths-

General

Easy

Question

After striking the floor, a certain ball redounds $open parentheses 4 divided by 5 close parentheses to the power of t h end exponent$ of height from which it has fallen. Then the total distance that it travels before coming to rest, if it is gently dropped from a height of 120 m is

1260 m
600 m
1080 m
None of these

The correct answer is: 1080 m

Initially the ball falls from a height of 120 m. After striking the floor, it rebounds and goes to a height of $fraction numerator 4 over denominator 5 end fraction cross times open parentheses 120 close parentheses$ m. Now, if falls from a height of $fraction numerator 4 over denominator 5 end fraction cross times open parentheses 120 close parentheses$ m and after rebounding goes to a height of $fraction numerator 4 over denominator 5 end fraction open parentheses fraction numerator 4 over denominator 5 end fraction open parentheses 120 close parentheses close parentheses$ m. This process is continued till the ball comes to rest
Hence, the total distance travelled is
$120 plus 2 open square brackets fraction numerator 4 over denominator 5 end fraction open parentheses 120 close parentheses plus open parentheses fraction numerator 4 over denominator 5 end fraction close parentheses to the power of 2 end exponent open parentheses 120 close parentheses plus horizontal ellipsis infinity close square brackets$
$equals 120 plus 2 open square brackets fraction numerator fraction numerator 4 over denominator 5 end fraction open parentheses 120 close parentheses over denominator 1 minus fraction numerator 4 over denominator 5 end fraction end fraction close square brackets equals 1080 blank m$

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