# write the resulting equation below, rounding to the nearest hundredth. determine the initial velocity of the baseball and the height of the ball when hit. round to the nearest hundredth. calculate...

write the resulting equation below, rounding to the nearest hundredth. determine the initial velocity of the baseball and the height of the ball when hit. round to the nearest hundredth. 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.

**A batter hits a fly ball. a scout in the stands makes the following observations.**

**TIME (SECONDS) .75 1.5 2 2.75 3.25 4.75**

**HEIGHT (FEET) 77 133 160 187 194 169**

What type of function that best models this data. use a graphing calculator to perform the regression for the best fit equation.

write the resulting equation below, rounding to the nearest hundredth.

determine the initial velocity of the baseball and the height of the ball when hit. round to the nearest hundredth.

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. show your work and round to the nearest hundredth.

*print*Print*list*Cite

### 1 Answer

Using the regression capabilities of a graphing calculator I found the best function to model this set of data to be a quartic with an `R^2` value of .99929. The cubic model had an `R^2` value of .9985, while the quadratic model had an `R^2` value of .9979

I am positive that in a beginning algebra class that the expectation is for the quadratic. (This actually models the entire flight of the ball better.)

The quadratic function is approximately:

`f(t)=-15.94t^2+110.20t+4.87`

**The height of the ball when hit is `f(0)=4.87` feet.**

To find the time when the ball is at 6 feet we set f(t)=6 and solve:

`-15.94t^2+110.2t+4.87=6`

`-15.94t^2+110.2t-1.13=0`

Using the quadratic formula we get:

`t=(-110.2+-sqrt(110.2^2-4(-15.94)(-1.13)))/(2(-15.94))`

`=(-110.2+-sqrt(12071.9912))/(-31.88)`

`=.0103` or `6.9032`

Since t=.01 seconds is immediately after the ball was hit, the **outfielder has 6.90 seconds to get into position.**

(Alternatively you could graph the parabola and the line y=6 in the graphing utility and find the intersection: in my calculator I got 6.90 seconds.)