SITE-C teams: Lesson 18

A block of ice slides down a 100 foot chute with an acceleration of 16 ft. / sec2. The distance of the block from the bottom of the chute is given by the formula:

s(t) = 100 - 20 t - 8 t2

How long does it take the block of ice to slide 12 feet? What is the velocity of the block at this point? How long does it take to reach the bottom of the chute?

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 100 - 20 X - 8 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 F3 (V-Window) to set the parameters as follows:

 Xmin = 0 Ymin = -20 Xmax = 3.15 Ymax = 108.5 Xscale = 0.25 Yscale = 20

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 F1 (Trace) and use the right cursor arrow to move to where the y value is 88. At 0.5 seconds (the x value), the block of ice has gone 12 feet ( = 100 - 88 ) down the slide and has a velocity of 28 ft./ sec. (the dY / dX value) moving down the slide.

Press the right cursor arrow until the y value is zero (the end of the chute). At this point x = 2.5 and dY / dX = -60 so the block of ice reaches the bottom of the chute in 2.5 seconds (the x value) and has a velocity at that point of 60 ft. / sec. (the dY / dX value).