Chapter 4: Parametric Graphing 133
Chapter 4:
Chapter 4:Chapter 4:
Chapter 4:
Parametric Graphing
Parametric GraphingParametric Graphing
Parametric Graphing
Getting Started: Path of a Ball
Getting Started: Path of a BallGetting Started: Path of a Ball
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
2
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