Operation Manual

Chapter 4: Parametric Graphing 95
Chapter 4:
Parametric Graphing
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 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
o
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 gt
2
The vertical and horizontal vectors of the ball’s motion also will be graphed.
Vertical vector:
Horizontal vector:
Gravity constant:
X2(t)=0
X3(t)=X1(t)
g=9.8 m/sec
2
Y2(t)=Y1(t)
Y3(t)=0
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. Go to the Format Graph screen, and turn off the axes.
• Press
y. to go to the Format Graph screen.
Press †††† to select
Axes, the spinner menu
becomes active. Press |
as necessary to turn off the axes.
3. Press o. Press
30 „ ™ 25 y; 1 (to select ¡)
¤Í to define
X1T in terms of T.
4. Press
30 „ ˜ 25 y ; 1 ¤ ¹ t ^ 1 (to select
n/d) 9.8 ~ 2 ~ „ ¡ Í to define Y1T.
1
2
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