Texas Instruments TI-83 Getting Started: Path of a Ball

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 v0 and angle q, the position of the ball as a function of time
has horizontal and vertical components.
Horizontal: X1(t) =tv0cos(q)
Vertical: Y1(t) =tv0sin(q)N 1
2 gt2
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/sec2
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
X1T in terms of T.
3. Press 30 „ ˜ 25 y [ANGLE] 1 ¤ ¹
9.8 ¥ 2 „ ¡ Í to define Y1T.
The vertical component vector is defined
by X2T and Y2T.
4. Press 0 Í to define X2T.
5. Press  ~ to display the VARS Y.VARS
menu. Press 2 to display the PARAMETRIC
secondary menu. Press 2 Í to define
Y2T.
Getting Started: Path of a Ball