Before a football game, a coin toss is used to determine which team will kick off. The height h (in feet) of a coin above the ground t seconds after being flipped up into the air is given by h = −16t2 + 54t + 7. How long will the coin be in the air?

T(t)  =  3,375 s

Step-by-step explanation:

Trajectory equation for the coin is:

h(t)  = - 16*t² + 54*t  + 7

Then speed of the coin is  Dh/dt

D(h) / dt =  - 32*t  + 54

When  

D(h) / dt = 0     the coin get maximum height

So    - 32*t   +  54  = 0  we solve for t

- 32*t  = - 54     ⇒  t  = 54 / 32      ⇒  t = 1,6875 s

Then time for the coin to get maximum height is 1,6875 seconds

The coin will take the same time t traveled from maximum height to ground. Therefore the coin will take 2 times t in the air

Total time in the air (Tt) = 2*1,6875 s

T(t)  =  3,375 s

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step-by-step explanation:

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