Calculate how many seconds an outfielder has to position himself for the catch if he intends to catch the ball 6 feet above the groundTime(sec) .75 1.5 2 2.75 3.25 4.75 Height(ft) 77 133 160 187...

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

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jerichorayel | College Teacher | (Level 2) Senior Educator

Posted on

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. 

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