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Question

After striking the floor ball rebounds 45th of its height from which it has fallen. If it is released from a height of 120m, then the total distance travelled by the ball (in m) before it comes to rest is


A
960
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B
1000
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C
1080
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D
2040
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Solution

The correct option is C 1080
Except the first fall, the ball will travel the same distance twice (upward and downward) in each step.
Total distance =h+2[4h5+42h52+]
=120+2[120×45+120×(45)2+120×(45)3+...]
=120+240[45+(45)2+(45)3+...]
=120+240⎢ ⎢ ⎢45145⎥ ⎥ ⎥=120+960=1080 m 

Mathematics

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