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An engineer designed a ball so that when it was dropped, it rose with

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An engineer designed a ball so that when it was dropped, it rose with  [#permalink]

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New post 24 Aug 2016, 05:21
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A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

68% (02:12) correct 32% (02:16) wrong based on 194 sessions

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An engineer designed a ball so that when it was dropped, it rose with each bounce exactly one-half as high as it had fallen. The engineer dropped the ball from a 16-meter platform and caught it after it had traveled 46.5 meters. How many times did the ball bounce?

A. 5
B. 6
C. 7
D. 8
E. 9

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Re: An engineer designed a ball so that when it was dropped, it rose with  [#permalink]

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New post 24 Aug 2016, 05:49
Bunuel wrote:
An engineer designed a ball so that when it was dropped, it rose with each bounce exactly one-half as high as it had fallen. The engineer dropped the ball from a 16-meter platform and caught it after it had traveled 46.5 meters. How many times did the ball bounce?

A. 5
B. 6
C. 7
D. 8
E. 9



Bounce count Distance traveled Total distance traveled
_____1_______16__________________16
_____2_______8 (rise) + 8 (fall________32
_____3_______4(rise) + 4(fall)________40
_____4_______2(rise) + 2(fall)________44
_____5_______1 + 1_______________46
_____6_______0.5 + 0.5____________47

Hence 6 bounces. Answer is B





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Re: An engineer designed a ball so that when it was dropped, it rose with  [#permalink]

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New post 24 Aug 2016, 06:13
Going down = 16 m

Going Up = 8 --> Total = 24

Going down = 8 --> Total = 32


Going Up = 4 --> Total = 36

Going down = 4 --> Total = 40

Going up = 2 --> Total = 42

Going down = 2 --> Total = 44

Going up = 1 --> Total = 45

Going down = 1 --> Total = 46

Going up = 0.5 --> Total = 46.5 (Caught)

No of going downs = 5 .. Option A
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Re: An engineer designed a ball so that when it was dropped, it rose with  [#permalink]

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New post 24 Aug 2016, 23:32
the solution can be written as 16,8,8,4,4,2,2,1,1,.5 with every odd number being a bounce.hence 5

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Re: An engineer designed a ball so that when it was dropped, it rose with  [#permalink]

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New post 09 Mar 2017, 09:39
Wow... I can't believe I didn't think of calculating the balls travel distance as it bounced up.
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Re: An engineer designed a ball so that when it was dropped, it rose with  [#permalink]

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New post 15 Mar 2017, 16:42
Bunuel wrote:
An engineer designed a ball so that when it was dropped, it rose with each bounce exactly one-half as high as it had fallen. The engineer dropped the ball from a 16-meter platform and caught it after it had traveled 46.5 meters. How many times did the ball bounce?

A. 5
B. 6
C. 7
D. 8
E. 9


An efficient way to solve to this problem is to keep track of the distance the ball traveled in each bounce and the cumulative total distance it traveled.

1st bounce: 16 meters down and 8 meters up → traveled 24 meters

2nd bounce: 8 meters down and 4 meters up → traveled 12 meters + 24 meters earlier = 36 meters

3rd bounce: 4 meters down and 2 meters up → traveled 6 meters + 36 meters earlier = 42 meters

4th bounce: 2 meters down and 1 meter up → traveled 3 meters + 42 meters earlier = 45 meters

5th bounce: 1 meter up and 0.5 meter down → traveled 1.5 meters + 45 meters earlier = 46.5 meters

Answer: A
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Re: An engineer designed a ball so that when it was dropped, it rose with  [#permalink]

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New post 01 Jul 2017, 16:40
Answer is 5 bounces
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bounce.jpg
bounce.jpg [ 58.78 KiB | Viewed 1232 times ]


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Re: An engineer designed a ball so that when it was dropped, it rose with  [#permalink]

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Re: An engineer designed a ball so that when it was dropped, it rose with   [#permalink] 17 Sep 2018, 04:12
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