Getting Started: Path Of A Ball - Texas Instruments TI-82 STATS Manual Book

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
horizontal and vertical components.
Horizontal:
Vertical:
The vertical and horizontal vectors of the ball's motion also will be graphed.
Vertical vector:
Horizontal vector:
Gravity constant:
1. Press z. Press † † † ~ Í to select
mode. Press † † ~ Í to select
Par
for simultaneous graphing of all three
Simul
parametric equations in this example.
2. Press o. Press
(to select ¡) ¤ Í to define
[ ]
1
ANGLE
in terms of .
T
„ ˜
3. Press
30
¥ „ ¡ Í to define
9.8 2
The vertical component vector is defined by
and .
X Y
2T 2T
Í to define
4. Press
0
5. Press  ~ to display the
menu. Press to display the
2
secondary menu. Press
4-2 Parametric Graphing
and angle q, the position of the ball as a function of time has
0
X1(t)=tv cos(q)
0
Y1(t)=tv sin(q)N
0
X2(t)=0
X3(t)=X1(t)
2
g=9.8 m/sec
„ ™
30 25
y [
25
ANGLE
.
X
2T
VARS Y.VARS
PARAMETRIC
Í to define
2
1
2
gt
2
Y2(t)=Y1(t)
Y3(t)=0
y
X
1T
¤ ¹
]
1
.
Y
1T
.
Y
2T