Texas Instruments PLUS TI-89 - Manual (Page 145)

128 Chapter 7: Parametric Graphing
07PARAM.DOC TI-89/TI-92 Plus: Parametric Graphing (English) Susan Gullord Revised: 02/23/01 10:56 AM Printed: 02/23/01 2:13 PM Page 128 of 6
Steps
³
TI-89
Keystrokes
›
TI-92 Plus
Keystrokes Display
1. Display the MODE dialog box.
For Graph mode, select
PARAMETRIC .
3
B 2
¸ 3
B 2
¸
2. Display and clear the Y= Editor.
Then define the horizontal
component
xt1(t) = v
0
t cos q .
Enter values for v
0
and q .
TI - 89: T ype T p 2 X , not
T 2 X .
TI - 92 Plus: Type T p X , not T X .
Enter a ¡ symbol by typing either
2 “ or 2 I 2 1 . This ensures a
number is interpreted as degrees,
regardless of the angle mode.
¥ #
ƒ 8 ¸
¸
1 5 T p
2 X 6 0
2 “d ¸ ¥ #
ƒ 8 ¸
¸
1 5 T p
X 6 0
2 “d ¸ xt1(t)=15tù cos(60 ¡)
3. Define the vertical component
yt1(t) = v
0
t sin q – (g/2)t 2 .
Enter values for v
0
, q , and g.
¸
1 5 T p
2 W 6 0
2 “d | c
9 . 8 e 2 d
T Z 2 ¸ ¸
1 5 T p
W 6 0
2 “d | c
9 . 8 e 2 d
T Z 2 ¸
4. Display the Window Editor.
Enter Window variables
appropriate for this example.
You can press either D or ¸ to
enter a value and move to the next
variable.
¥ $
0 D 3 D
. 0 2 D · 2 D
2 5 D 5 D
· 2 D 1 0 D
5 ¥ $
0 D 3 D
. 0 2 D · 2 D
2 5 D 5 D
· 2 D 1 0 D
5
5. Graph the parametric equations
to model the path of the ball.
¥ % ¥ %
6. Select Trace . Then move the
cursor along the path to find the:
¦ y value at maximum height.
¦ t value where the ball hits the
ground.
…
B or A
as necessary
…
B or A
as necessary
Preview of Parametric Graphing
Graph the parametric equations describing the path of a ball kicked at an angle ( q ) of 60 ¡
with an initial velocity (v
0
) of 15 meters/sec. The gravity constant g = 9.8 meters/sec 2 .
Ignoring air resistance and other drag forces, what is the maximum height of the ball and
when does it hit the ground?