Calculate how many seconds an outfielder has to position himself for the catch if he intends to catch the ball 6 feet above the ground
Time(sec) .75 1.5 2 2.75 3.25 4.75
Height(ft) 77 133 160 187 194 169
Using the linear regression from the calculator the quadratic function for this set of data is:
f(t) = -15.94t^2 + 110.20 t + 4.87
We find the time when the ball is 6 feet above the ground, thus we have to set f(t) = 6.
6 = -15.94t^2 + 110.20 t + 4.87
(0 = -15.94t^2 + 110.20 t -1.13) -1
0 = 15.94t^2 - 110.20 t + 1.13
a b c
Then we can use the quadratic formula to solve the answer.
`t = (-b +- sqrt(b^2-4ac))/(2a) `
by substituting the values of a, b and c, we can get the value of t = 6.903 and 0.0102 seconds. Quadratic equations have two answers and you have to choose the later one.
You will have 6.903 seconds to get into the position.