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30 Aug 2019, 23:50
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Difficulty:
35%
(medium)
Question Stats:
82% (01:08) correct
18%
(01:50)
wrong
based on 34
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If a rubber ball consistently bounces back \(\frac{2}{3}\) of the height from which it is dropped, what fraction of its original height will the ball bounce after being dropped and bounced four times without being stopped?
A. \(\frac{16}{81}\)
B. \(\frac{16}{27}\)
C. \(\frac{4}{9}\)
D. \(\frac{37}{81}\)
E. \(\frac{9}{12}\)
A. \(\frac{16}{81}\)
B. \(\frac{16}{27}\)
C. \(\frac{4}{9}\)
D. \(\frac{37}{81}\)
E. \(\frac{9}{12}\)
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Where to now? Join ongoing discussions on thousands of quality questions in our Problem Solving (PS) Forum
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31 Aug 2019, 01:17
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DisciplinedPrep
If a rubber ball consistently bounces back \(\frac{2}{3}\) of the height from which it is dropped, what fraction of its original height will the ball bounce after being dropped and bounced four times without being stopped?
A. \(\frac{16}{81}\)
B. \(\frac{16}{27}\)
C. \(\frac{4}{9}\)
D. \(\frac{37}{81}\)
E. \(\frac{9}{12}\)
A. \(\frac{16}{81}\)
B. \(\frac{16}{27}\)
C. \(\frac{4}{9}\)
D. \(\frac{37}{81}\)
E. \(\frac{9}{12}\)
Given: A rubber ball consistently bounces back \(\frac{2}{3}\) of the height from which it is dropped.
Asked: What fraction of its original height will the ball bounce after being dropped and bounced four times without being stopped?
Let us assume that height from which the ball is dropped = x
After first bounce, height = \((\frac{2}{3})*x\)
After second bounce, height = \((\frac{2}{3})^2*x\)
After third bounce, height = \((\frac{2}{3})^3*x\)
After fourth bounce, height = \((\frac{2}{3})^4*x = (\frac{16}{81})*x\)
IMO A
31 Aug 2019, 10:56
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DisciplinedPrep
If a rubber ball consistently bounces back \(\frac{2}{3}\) of the height from which it is dropped, what fraction of its original height will the ball bounce after being dropped and bounced four times without being stopped?
A. \(\frac{16}{81}\)
B. \(\frac{16}{27}\)
C. \(\frac{4}{9}\)
D. \(\frac{37}{81}\)
E. \(\frac{9}{12}\)
A. \(\frac{16}{81}\)
B. \(\frac{16}{27}\)
C. \(\frac{4}{9}\)
D. \(\frac{37}{81}\)
E. \(\frac{9}{12}\)
Let Initial height be 81 m (There are 4 drops , and denominator is 3, So took initial height as 3^4)
Height after 1st Fall is 54m
Height after 2nd Fall is 36m
Height after 3rd Fall is 24m
Height after 4th Fall is 16m
So, Fraction of height gained after 4th fall is 16/81 , Answer must be (A)
Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Problem Solving (PS) Forum
Still interested in this question? Check out the "Best Topics" block above for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
