SITE-C teams: Lesson 10

A young pitcher throws a baseball straight up into the air with a velocity of 100 feet per second. Because of the gravitational pull of the earth the baseball’s height above the earth can be modeled by the formula h(x) = 100 x - 16 x^{2}.

What is the maximum height that the baseball reaches? How many seconds does it take for the baseball to achieve that height? What is its velocity at that time? What is the velocity of the baseball when it is 126 feet above the ground going up and then again coming down?

Turn on the **CASIO CFX-9850G** by pressing

Use the cursor arrows to highlight the GRAPH menu and press **EXE **or just press **5** when at the main menu screen.

In the Y1 slot enter 100 X - 16 X^{2} and press **EXE** to store it in memory.

Press **SHIFT** **MENU** (SETUP), use the down cursor arrow to scroll down and highlight the Derivative line, press **F1** (ON) **EXIT**.

Press **SHIFT** and **F3** (V-Window) to set the parameters as follows:

Xmin = 0 Ymin = -50 |
Xmax = 6.3 Ymax = 310 |
Xscale = 0.5 Yscale = 50 |

Press **EXIT** to return to the function list. Make sure that no other Y-slot is highlighted, i.e. selected for drawing. Press **F6** (DRAW) to see the graph.

Press **SHIFT** **F2** (ZOOM) **F1** (BOX). Use the cursor arrows to move the cross hairs to a desired location for the top left-hand corner of the box, for example x = 3.05 and y = 164.83870967, press **EXE** to mark this position. Use the cursor arrows to move the cross hairs to a desired location for the bottom right-hand corner of the box, for example x = 3.2 and y = 153.22580645, press **EXE**.

Press** SHIFT F1** (Trace) and use the right cursor arrow to approach the maximum y-value. This occurs at x = 3.125 and y = 156.25. Note that dY/dX = 0. This indicates that the baseball reaches its maximum height in 3.125 seconds and that height is 156.25 feet above the ground. Furthermore, the velocity of the baseball when it reaches that maximum is 0 ft/sec.

Press **SHIFT F2** (ZOOM) **F6** ( |> ) **F1** (ORIG) to return to the original viewing window.

Press** SHIFT F1** (Trace) and use the right cursor arrow to approach 126 feet off the ground going up (i.e., x = 1.75 and y = 126). The dY/dX = 44 so the velocity of the baseball at 126 ft going up is 44 ft/sec. Continue using the right cursor arrow to approach the 126 feet off the ground going down (i.e., x = 4.5 and y = 126). The dY/dX = -44 so the velocity of the baseball at 126 ft going down is 44 ft/sec. Note the negative sign indicates "going down."

Press **EXIT** **MENU**.

Turn off the **CASIO CFX-9850G** by pressing