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4-2 Parametric Graphing
8304PARA.DOC TI-83 international English Bob Fedorisko Revised: 02/19/01 12:17 PM Printed: 02/19/01 1:36
PM Page 2 of 8
Getting Started is a fast-paced introduction. Read the chapter for details.
Graph the parametric equation that describes the path of a ball hit at an initial
speed of 30 meters per second, at an initial angle of 25 degrees with the
horizontal from ground level. How far does the ball travel? When does it hit the
ground? How high does it go? Ignore all forces except gravity.
For initial velocity v
0
and angle
q
, the position of the ball as a function of time
has horizontal and vertical components.
Horizontal: X1(t)=tv
0
cos(
q
)
Vertical: Y1(t)=tv
0
sin(
q
)
N
1
2
gt
2
The vertical and horizontal vectors of the ball’s motion also will be graphed.
Vertical vector: X2(t)=0 Y2(t)=Y1(t)
Horizontal vector: X3(t)=X1(t) Y3(t)=0
Gravity constant: g=9.8 m/sec
2
1. Press
z
. Press
†
†
†
~
Í
to
select
Par mode. Press
†
†
~
Í
to
select
Simul for simultaneous graphing of
all three parametric equations in this
example.
2. Press
o
. Press 30
„
™
25
y
[
ANGLE
] 1 (to select
¡
)
¤
Í
to define
X
1T
in terms of T.
3. Press
30
„
˜
25
y
[
ANGLE
] 1
¤
¹
9.8
¥
2
„
¡
Í
to define Y
1T
.
The vertical component vector is defined
by
X
2T
and Y
2T
.
4. Press
0
Í
to define X
2T
.
5. Press
~
to display the
VARS Y
.
VARS
menu. Press 2 to display the
PARAMETRIC
secondary menu. Press 2
Í
to define
Y
2T
.
Getting Started: Path of a Ball