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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

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by AAPL » Wed Mar 17, 2021 7:14 am
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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 of the penny (how fast Hugo throws is 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

OA C
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Source: — Problem Solving |

AAPL wrote: ↑
Wed Mar 17, 2021 7:14 am


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 of the penny (how fast Hugo throws is 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

OA C
Solution:

We can create the equation:

60 = 20t + 5t^2

12 = 4t + t^2

t^2 + 4t - 12 = 0

(t + 6)(t - 2) = 0

t = -6 or t = 2

Since t can’t be negative, t = 2.

Answer: C

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