Question

I have a word problem here.

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

Time (in secs) .75, 1.5, 2, 2.75, 3.25, and 4.75

Height (in feet) 77, 133, 160, 187, 194, and 169

1.What type of function best models this data?

Linear, Exponential, Quadratic, or some other

2.Use a graphing calculator to perform the regression for the best-fit equation. Write the resulting equation, round to the nearest hundredth.

3. Determine the initial velocity of the baseball and the height of the ball when hit. Round to the nearest hundredth.

4. Calculate how many secs an outfielder has to position himself for the catch if he intends to catch the ball 6 feet above the ground. Show work and round to the nearest hundredth.

Thank you for your help. :)

Answer 1

1. Quadratic.

2. h = Yo*0.75 - 16.2*0.75^2 = 77 Ft.
Yo*0.75 - 9.11 = 77
0.75Yo = 86.11
Yo = 114.82 Ft/s.

Y = Yo + g*Tr = 0 @ max. ht.
Tr=(Y-Yo)/g = (0-114.82)/-32.4 = 3.54s.
= Rise time.

hmax = Yo*Tr + 0.5g*Tr^2
hmax=114.82*3.54 - 16.2*3.54^2=203.8 Ft.

Eq: h = -16.2t^2 + 114.82t