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# Hugo lies on top of a building, throwing pennies straight down to the

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Math Expert
Joined: 02 Sep 2009
Posts: 50007
Hugo lies on top of a building, throwing pennies straight down to the  [#permalink]

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03 Jul 2015, 02:59
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Difficulty:

15% (low)

Question Stats:

82% (01:46) correct 18% (02:12) wrong based on 99 sessions

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Hugo lies on top of a building, throwing pennies straight down to the street below. The formula for the height, H, that a penny falls is $$H= Vt+ 5t^2$$, where V/is the original velocity o f the penny (how fast Hugo throws it when it leaves his hand) and t is equal to the time it takes to hit the ground. The building is 60 meters high, and Hugo throws the penny down at an initial speed of 20 meters per second. How long does it take for the penny to hit the ground?

A. 2/5 seconds
B. 1 second
C. 2 seconds
D. 5 seconds
E. 6 seconds

Kudos for a correct solution.

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Re: Hugo lies on top of a building, throwing pennies straight down to the  [#permalink]

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03 Jul 2015, 03:46
Bunuel wrote:
Hugo lies on top of a building, throwing pennies straight down to the street below. The formula for the height, H, that a penny falls is $$H= Vt+ 5t^2$$, where V/is the original velocity o f the penny (how fast Hugo throws it when it leaves his hand) and t is equal to the time it takes to hit the ground. The building is 60 meters high, and Hugo throws the penny down at an initial speed of 20 meters per second. How long does it take for the penny to hit the ground?

A. 2/5 seconds
B. 1 second
C. 2 seconds
D. 5 seconds
E. 6 seconds

Kudos for a correct solution.

Solution -
Given that, H=60m, V=20m/s and t=?
Substitute above values in the given equation -> 60=20t+5t^2 -> t^2-2t+6t-12=0 -> (t-2)(t+6) =0

t = 2, -6. Time can not be in -ve value so ANS C.
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Hugo lies on top of a building, throwing pennies straight down to the  [#permalink]

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03 Jul 2015, 10:05
Plug each answer into the equation, $$60 = 20t + 5t^{2}$$, and two is the only answer. This can be done all mentally, as well.

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Re: Hugo lies on top of a building, throwing pennies straight down to the  [#permalink]

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03 Jul 2015, 11:21
60 = 20t + 5t^2

Now dont solve quadrtic ... better just plug options .
Option C , t= 2 is correct
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Hugo lies on top of a building, throwing pennies straight down to the  [#permalink]

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03 Jul 2015, 20:45
Bunuel wrote:
Hugo lies on top of a building, throwing pennies straight down to the street below. The formula for the height, H, that a penny falls is $$H= Vt+ 5t^2$$, where V/is the original velocity o f the penny (how fast Hugo throws it when it leaves his hand) and t is equal to the time it takes to hit the ground. The building is 60 meters high, and Hugo throws the penny down at an initial speed of 20 meters per second. How long does it take for the penny to hit the ground?

A. 2/5 seconds
B. 1 second
C. 2 seconds
D. 5 seconds
E. 6 seconds

Kudos for a correct solution.

Given : $$H= Vt+ 5t^2 = t*(V+5t)$$

H = 60 m
V = 20 m/s

Checking Options

A. 2/5 seconds $$H= t*(V+5t) = (2/5)(20+5*2/5) = 44/5$$ which is not equal to 60 so INCORRECT Option

B. 1 second $$H= t*(V+5t) = (1)(20+5*1) = 25$$ which is not equal to 60 so INCORRECT Option

C. 2 seconds $$H= t*(V+5t) = (2)(20+5*2) = 60$$ Since it matches the Given height H = 60 so CORRECT Option

D. 5 seconds
E. 6 seconds

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Hugo lies on top of a building, throwing pennies straight down to the  [#permalink]

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03 Jul 2015, 20:55
Bunuel wrote:
Hugo lies on top of a building, throwing pennies straight down to the street below. The formula for the height, H, that a penny falls is $$H= Vt+ 5t^2$$, where V/is the original velocity o f the penny (how fast Hugo throws it when it leaves his hand) and t is equal to the time it takes to hit the ground. The building is 60 meters high, and Hugo throws the penny down at an initial speed of 20 meters per second. How long does it take for the penny to hit the ground?

A. 2/5 seconds
B. 1 second
C. 2 seconds
D. 5 seconds
E. 6 seconds

Kudos for a correct solution.

the equation that is formed by putting values..
60=20t+5t^2..
here t has to be even integer so as to make 5t^2 a multiple of 10..
only C and E left..
Also t has to be <3 as otherwise RHS> 60 so E out
ans 2,
2 and 6 can be substituted too find the correct answer
ans C
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3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

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Re: Hugo lies on top of a building, throwing pennies straight down to the  [#permalink]

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04 Jul 2015, 09:15
Option C correct
Placing H=60 and V=20

we get t=2,-6
2 is correct
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Posts: 50007
Re: Hugo lies on top of a building, throwing pennies straight down to the  [#permalink]

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06 Jul 2015, 04:56
Bunuel wrote:
Hugo lies on top of a building, throwing pennies straight down to the street below. The formula for the height, H, that a penny falls is $$H= Vt+ 5t^2$$, where V/is the original velocity o f the penny (how fast Hugo throws it when it leaves his hand) and t is equal to the time it takes to hit the ground. The building is 60 meters high, and Hugo throws the penny down at an initial speed of 20 meters per second. How long does it take for the penny to hit the ground?

A. 2/5 seconds
B. 1 second
C. 2 seconds
D. 5 seconds
E. 6 seconds

Kudos for a correct solution.

MANHATTAN GMAT OFFICIAL SOLUTION:

H = Wt + 5t^2
60 = 20t+5t^2
5(t + 6)(t - 2) = 0

t = -6 or t = 2.

Since a time must be positive, discard the negative value for t.

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Re: Hugo lies on top of a building, throwing pennies straight down to the  [#permalink]

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24 Oct 2017, 05:57
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Re: Hugo lies on top of a building, throwing pennies straight down to the &nbs [#permalink] 24 Oct 2017, 05:57
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