Chapter 4: Parametric Graphing
91
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. Press
† † †† † † ~ Í
to go to the Format
Graph screen. Press
† † † ~ Í
to select
AxesOff
, which turns off the axes.
1
2
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