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 the following equation.
h = -16t2 + 34t + 15.
How long does a team captain have to call heads or tails if it must be done while the coin is in the air?
seconds
Ask for what t is -16t^2 + 34t + 15 = 0? Use the usual quadratic formula for that one:
x = (-b +/- sqrt(b^2 - 4ac)) / 2a
sqrt(b^2 - 4ac) = 46, so the answer is either a negative number or 80/32 = 10/4 = 2.5. So that's the answer: two and a half seconds.
To determine how long the team captain has to call heads or tails, we need to find the time when the coin reaches its maximum height. At the highest point, the coin is momentarily at rest before it starts falling back down.
The equation given to calculate the height of the coin is h = -16t^2 + 34t + 15. To find the time when the coin reaches its maximum height, we need to find the vertex of this quadratic equation.
The vertex of a quadratic equation in the form ax^2 + bx + c is given by the formula: x = -b / (2a). In this case, a = -16 and b = 34.
Substituting the values into the formula, we have:
t = -34 / (2 * -16)
= -34 / -32
= 1.0625
The team captain has approximately 1.0625 seconds to call heads or tails.