SOLUTION: A ball always bounces three fifth of the height from which it falls. What fraction of its initial height does it rise after the second and third bounce?

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: A ball always bounces three fifth of the height from which it falls. What fraction of its initial height does it rise after the second and third bounce?      Log On


   

Question 1144812: A ball always bounces three fifth of the height from which it falls. What fraction of its initial height does it rise after the second and third bounce?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +n+ = the number of bounces
Let +h+ = the height after +n+ bounces
Let +h%5B0%5D+ = the starting height
+h+=+h%5B0%5D%2A%28+1+-+2%2F5+%29%5En+
+h+=+h%5B0%5D%2A%28+3%2F5+%29%5En+
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After 2nd bounce:
+h+=+h%5B0%5D%2A%28+3%2F5+%29%5E2+
+h%2Fh%5B0%5D+=+9%2F25+
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After 3rd bounce:
+h+=+h%5B0%5D%2A%28+3%2F5+%29%5E3+
+h%2Fh%5Bo%5D+=+27%2F125+