Operation Manual

4-2 Parametric Graphing
8204PARA.DOC TI-82, Chapter 4, English Bob Fedorisko Revised: 02/09/01 9:08 AM Printed: 02/09/01
12:37 PM Page 2 of 6
Getting Started: Path of a Ball
Getting Started is a fast-paced introduction. Read the chapter for details.
Graph the parametric equation that describes the position of a ball kicked at an
angle of 60
¡
with an initial velocity of 15 meters per second. (Ignore air
resistance.) What is the maximum height? When does the ball strike the ground?
1. Press
z
. Press
† † † ~ Í
to select
Par
MODE
.
For initial velocity v
0
and angle
q
, the horizontal
component of the position of the ball as a
function of time is X(t)=tv
0
cos
q
. The vertical
component is Y(t)=tv
0
sin
q
–(g
à
2)t
2
. The gravity
constant g is 9.8 m/sec
2
.
2. Press
o
. Press
15
„ ™
60
y
ã
ANGLE
ä
1
(to select
¡
)
Í
to define the
X
portion of the
parametric equation in terms of
T
.
3. Press
15
„ ˜
60
y
ã
ANGLE
ä
1
(to select
¡
)
¹ £
9.8
¥
2
¤ „ ¡ Í
to define the
Y
portion.
4. Press
p
. Press
†
to move to
Tmin
and
then enter the
WINDOW
variables appropriate
for this problem.
Tmin=0 Xmin=-2 Ymin=-2
Tmax=3 Xmax=25 Ymax=10
Tstep=.02 Xscl=5 Yscl=5
5. Press
r
to graph the position of the ball as
a
function of time.
Tracing begins at
Tmin
. As you press
~
to trace
the curve, the cursor follows the path of the ball
over time. The values for
X
(distance),
Y
(height), and
T
(time) are displayed at the
bottom of the screen.