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dexar [7]
3 years ago
13

A Nerf gun is shot straight up from the ground with an initial velocity of 14.0 m/s. What is the total time the projectile is in

the air?
PLEASE SHOW WORK WILL MARK BRAINLIEST
Physics
1 answer:
Sergeeva-Olga [200]3 years ago
7 0

The projectile has a height <em>h</em> at time <em>t</em> given by

<em>h</em> = (14.0 m/s) <em>t</em> - 1/2 <em>g t</em> ²

where <em>g</em> = 9.80 m/s² is the magnitude of the acceleration due to gravity. Solve for <em>t</em> when <em>h</em> = 0 :

0 = (14.0 m/s) <em>t</em> - 1/2 <em>g t</em> ²

0 = 1/2 <em>t</em> (28.0 m/s - <em>g t</em> )

1/2 <em>t</em> = 0   <u>or</u>   28.0 m/s - <em>g</em> <em>t</em> = 0

The first equation says <em>t</em> = 0, which refers to the moment the gun is first fired, so we ignore that solution. We're left with

28.0 m/s - <em>g t</em> = 0

<em>t</em> = (28.0 m/s) / <em>g</em>

<em>t</em> = (28.0 m/s) / (9.80 m/s²)

<em>t</em> ≈ 2.86 s

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Calculating the value of negative displacement upon the time t:

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\to X= X_{+ve} + X_{-ve} \\\\

\to  150 - 50 -20t+400 =0\\\\\to 100 -20t+400 =0 \\\\\to 500 -20t =0\\\\\to 20t =500 \\\\\to t=\frac{500}{20}\\\\\to t=\frac{50}{2}\\\\\to t= 25

That's why its value lie in "between 20 s and 30 s".

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soldi70 [24.7K]

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Explanation:

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\:\:\:\:\:\:\:= 5.1\:\text{m}

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