MATH 1101: Modeling the Flight of a Baseball -- Page 4

Modeling the Flight of a Baseball

The Problem

A baseball is hit upward with an initial velocity of = 80 feet per second (or about 55 miles per hour) and leaves the bat with an initial height of = 3 feet.

a). Write a formula s(t) that models the height of the baseball after t seconds.
b). How high was the baseball after 2 seconds?
c). Find the maximum height of the baseball. Support your answer graphically.

c. To find the maximum height of the baseball, the maximum point on the graph of s, or the vertex of the parabola, will be found. Press and enter function s as follows:

(Notice that x is the variable used on the TI83 for graphing purpose).

Now change the window settings to [-5, 10, 5] by [0, 120, 5]. Press GRAPH and the graph should appear as shown below.

Press 2nd TRACE and select 4:maximum. Using the LEFT ARROW KEY, move the cursor until it is slightly to the left of the maximum point on the graph and press ENTER.

Using the RIGHT ARROW KEY, move the cursor until it is slightly to the right of the maximum point and press ENTER. Using the LEFT ARROW KEY once more, move the cursor close to the actual maximum point and press ENTER. The results are show below.

The maximum point on the graph is (2.5, 103). Thus, the maximum height of the baseball is 103 feet (when t = 2.5 seconds).