SITE-C teams: Lesson 17

 

A rubber ball is bouncing straight up and down in such a way that its height above the ground, measured in feet, is given after t seconds by the formula

h(t) = ( 10 | cos t | ) ¸ (1 + t)

What is the velocity of the ball when it hits the ground for the first time. What is the maximum height that the ball attains after that first bounce? What is the approximate velocity of the ball after 28 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 ( 10 Abs (X) ) ¸ ( 1 + X) 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 = -4

Xmax = 31.5

Ymax = 12.4

Xscale = 5

Yscale = 2

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). To find the velocity when the ball first strikes the ground, use the cursor arrows to obtain a convenient point for the top left-hand corner of the box, say (1.25, 0.23225806451) and press EXE. Use the cursor arrows to obtain a convenient point for the bottom right-hand corner of the box, say (1.75, 0.2967741935) and press EXE.

Press SHIFT F1 (Trace) and use the right cursor arrow to move to where the y value is close to zero. At 1.5674603174 seconds (the x value), the ball is 0.0129933971 feet (the y value) off the ground coming down with a velocity of 3.899 ft./ sec. (the dY / dX value). Press the right cursor arrow one more time and you will see that at 1.5714285714 seconds (the x value), the ball is 0.00245872897 feet (the y value) above the ground going back up with a velocity of 3.8879 ft./ sec. (the dY / dX value).

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

Press SHIFT F5 (G-Solv) F2 (MAX) to obtain the maximum height that the ball attains after the first bounce. This is the y value 2.4897613487 feet and it is attained in 2.8899697028 seconds.

Press SHIFT F1 (Trace) and the right cursor arrow to move the cross hairs to x = 28. The velocity of the ball after 28 seconds is 0.0819 ft. / sec. (the dY / dX value) and it is going up.

Press EXIT MENU.

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