SITE-C teams: Lesson 12

 

From a top a 60 foot overpass, a brick is thrown straight up with a velocity of 20 feet per second. How long will it take to hit the ground below? With what velocity will the brick hit the ground? How high did the brick get and how long did it take to achieve that height?

The height in feet of the brick thrown vertically into the air can be expressed by the mathematical formula h(x) = 60 + 20 x - 16 x2 where x is time measured in seconds.

Turn on the CASIO CFX-9850G by pressing AC/ON.

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 60 + 20 X - 16 X2 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 = -10

Xmax = 3.15

Ymax = 77.5

Xscale = 0.5

Yscale = 10

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 the down cursor arrow to move the viewing window down.

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 = 2.625 and y = 1.2903225806, 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 = 2.675 and y = -1.5322580645, press EXE.

Press SHIFT F1 (Trace) and use the right cursor arrow to approach the root. This occurs at x = 2.6599206349 and y = -4.4318467E-3. Note that dY/dX = -65.11. This indicates that the brick strikes the ground in approximately 2.66 seconds with a velocity of 65.11 ft./sec.

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

Press SHIFT F5 (G-Solv) F2 (MAX). The brick reached a height of 66.25 ft. above the ground in 0.625 seconds.

Press EXIT MENU.

Turn off the CASIO CFX-9850G by pressing SHIFT AC/ON (OFF).