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 t seconds after being flipped up into the air is given by h=-16t^2+22t +3. How long does the team captain have to call heads or tails if it must be done while the coin is in the air?
Answer provided by our tutors
He has until it hits the ground, at h(t) = 0
or, -16t^2 + 22t + 20 = 0
Factor out a 2 from each coefficient to get:
-8t^2 + 11t + 10 = 0
Factors for this equation should be:
(8t + 5) * (-t + 2)= 0
-t = -2 which becomes t = 2
or you get:
8t = -5 which you reject right away because it's negative, and t can't be negative.
Your answer should be t = 2
This means that he gets 2 seconds to call heads or tails before the coin hits the ground.