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