Question 231484
Formula is:


h = -16t^2 + 22t + 20.


The amount of time he gets to call heads or tails is the amount of time that the coin is in the air.


The coin is in the air until h = 0.


At that point in time, the coin has touched the ground.


You need to solve your equation for:


-16t2 + 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


You get:


-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.


To test, replace t in the original equation with 2 and you should get h = 0


h = -16t2 + 22t + 20 becomes:


h = -16*4 + 22*2 + 20 = -64 + 44 + 20 = -64 + 64 = 0


It checks out so your answer is 2 seconds.


There is a more complicated answer but I don't think it's pertinent to the exercise so, for practical purposes, you can ignore that, and just use the formula as I showed you above.