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When a certain rubber ball is dropped, it rebounds 75 percent as high

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yrozenblum
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When a certain rubber ball is dropped, it rebounds 75 percent as high [#permalink] New post   14 Oct 2023, 11:10
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When a certain rubber ball is dropped, it rebounds 75 percent as high as the distance it fell. What is the approximate height from which the ball was dropped, if it had traveled a total of 2,146 centimeters vertically by the time it struck the ground for the third time?

A. 400 cm
B. 500 cm
C. 600 cm
D. 700 cm
E. 800 cm­


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C
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gmatophobia
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Re: When a certain rubber ball is dropped, it rebounds 75 percent as high [#permalink] New post   14 Oct 2023, 12:02
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yrozenblum wrote:
When a certain rubber ball is dropped, it rebounds 75 percent as high as the distance it fell. What is the approximate height from which the ball was dropped, if it had traveled a total of 2,146 centimeters vertically by the time it struck the ground for the third time?

A. 400 cm
B. 500 cm
C. 600 cm
D. 700 cm
E. 800 cm


  • Initial distance = \(d\)

After the first rebound

  • Distance travelled upward = \(\frac{3}{4} d\)
  • Distance travelled downward = \(\frac{3}{4} d\)

After the second rebound

  • Distance travelled upward = \((\frac{3}{4})^2 d\)
  • Distance travelled downward = \((\frac{3}{4})^2 d\)

Total vertical distance = \(d + 2*\frac{3}{4} d + 2*(\frac{3}{4})^2 d\)

\(d(1 + 2*\frac{3}{4} + 2*(\frac{3}{4})^2)\)

\(d(1 + \frac{3}{2} +\frac{9}{8})\)

\(d(1 + 1.5 +1.125)\) = \(3.625d\)

\(3.625d = 3 + \frac{625}{1000} = 3 + \frac{5}{8} = \frac{29}{8}d\)

\(\frac{29}{8}d = 2146 \)

\(d = 2146 * \frac{8}{29} = 74 * 8 = 592\)

Option C
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Focus7
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Re: When a certain rubber ball is dropped, it rebounds 75 percent as high [#permalink] New post   14 Oct 2023, 12:01
Can someone solve this ?

I was getting 2700 with c and around 2200 with b so decided to go with b

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Re: When a certain rubber ball is dropped, it rebounds 75 percent as high [#permalink] New post   23 Nov 2023, 10:17
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Quick question. You jump from 2146/29 being 74. Is there an easy technique to use to do this? Or have you gone through the process of actually working it out? Thank you!
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Re: When a certain rubber ball is dropped, it rebounds 75 percent as high [#permalink] New post   23 Nov 2023, 10:30
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jackg0101 wrote:
Quick question. You jump from 2146/29 being 74. Is there an easy technique to use to do this? Or have you gone through the process of actually working it out? Thank you!


Hey jackg0101

I solved it. We can use the long division approach, or we can use observation and approximation to choose a number. I used the latter one -

\(\frac{2146}{29} \approx \frac{2100}{30} \approx 70\)

So, the quotient will be in the range of 70's

Next, observe that 2146 ends with a 6 and 29 ends with a 9. As 4 * 9 = 36, I would multiply 74 and 29 to see if the resultant value is 2146.

\(74(30 - 1) = 2220 - 74 = 7146\)
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Re: When a certain rubber ball is dropped, it rebounds 75 percent as high [#permalink] New post   23 Nov 2023, 10:36
Ok great, thank you!
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Re: When a certain rubber ball is dropped, it rebounds 75 percent as high [#permalink] New post   23 Mar 2024, 13:21
The way I read this was that it traveled 2146cm only by adding up the vertical distance traveled.... So I was sitting here and nothing was adding up. Not sure how I am supposed to know it's talking about the distance going up and down when it literally says "traveled a total of 2146 centimeters vertically...."

Anyone else think this?
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Bunuel
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Re: When a certain rubber ball is dropped, it rebounds 75 percent as high [#permalink] New post   24 Mar 2024, 04:05
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Jake7Wimmer wrote:
When a certain rubber ball is dropped, it rebounds 75 percent as high as the distance it fell. What is the approximate height from which the ball was dropped, if it had traveled a total of 2,146 centimeters vertically by the time it struck the ground for the third time?

A. 400 cm
B. 500 cm
C. 600 cm
D. 700 cm
E. 800 cm

The way I read this was that it traveled 2146cm only by adding up the vertical distance traveled.... So I was sitting here and nothing was adding up. Not sure how I am supposed to know it's talking about the distance going up and down when it literally says "traveled a total of 2146 centimeters vertically...."

Anyone else think this?

­
Traveled vertically does not necessarily imply movement only in an upward direction. The term encompasses both upward and downward movements, as dropping down is also a vertical movement.
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Re: When a certain rubber ball is dropped, it rebounds 75 percent as high [#permalink]
24 Mar 2024, 04:05
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