Question

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.

Answer 1

y = -15.9x² + 110.48x + 3.02

initial velocity: 110.48 ft/s

initial height: 3.02 ft

time to cath the ball at 6 ft: 6.92

Explanation:

In the picture attached, the plot of the data points and the equation of the best regression is shown, which correspond to a quadratic equation. (It was obtained using Excel)

The initial velocity is the second coefficient.

The initial height is the third coefficient.

Replacing y = 6 into the equation and solving with the quadratic formula:

6 = -15.9x² + 110.48x + 3.02

0 = -15.9x² + 110.48x + 3.02 - 6

0 = -15.9x² + 110.48x - 2.98

`x = (-b \pm √(b^2 - 4ac))/(2a)`

`x = (-110.48 \pm √(110.48^2 - 4(-15.9)(-2.98)))/(2(-15.9))`

`x = (-110.48 \pm 109.62)/(-31.8)`

`x_1 = (-110.48 + 109.62)/(-31.8)`

`x_1 = 0.03`

`x_2 = (-110.48 - 109.62)/(-31.8)`

`x_2 = 6.92`

In the context of the problem, only x2 has sense.