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Texas Instruments ti 83 plus Manual

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17-12 Applications
8317APPS.DOC TI-83 international English Bob Fedorisko Revised: 02/19/01 1:00 PM Printed: 02/19/01 1:39 PM
Page 12 of 20
Using two pairs of parametric equations, determine when
two objects in motion are closest to each other in the same
plane.
A ferris wheel has a diameter (d) of 20 meters and is
rotating counterclockwise at a rate (s) of one revolution
every 12 seconds. The parametric equations below
describe the location of a ferris wheel passenger at time T,
where
a
is the angle of rotation, (0,0) is the bottom center
of the ferris wheel, and (10,10) is the passenger’s location
at the rightmost point, when T=0.
X(T) = r cos
a
where
a
= 2
p
Ts and r = d
à
2
Y(T) = r + r sin
a
A person standing on the ground throws a ball to the ferris
wheel passenger. The thrower’s arm is at the same height as
the bottom of the ferris wheel, but 25 meters (b) to the right
of the ferris wheel’s lowest point (25,0). The person throws
the ball with velocity (v
0
) of 22 meters per second at an
angle (
q
) of 66
¡
from the horizontal. The parametric
equations below describe the location of the ball at time T.
X(T) = b
N
Tv
0
cos
q
Y(T) = Tv
0
sin
q
N
(g
à
2) T
2
where g =
9.8 m/sec
2
1. Press
z
. Select Par, Simul, and the default settings.
Simul (simultaneous) mode simulates the two objects in
motion over time.
2. Press
p
. Set the viewing window.
Tmin=0 Xmin=
L
13 Ymin=0
Tmax=12 Xmax=34 Ymax=31
Tstep=.1 Xscl=10 Yscl=10
3. Press
o
. Turn off all functions and stat plots. Enter the
expressions to define the path of the ferris wheel and the
path of the ball. Set the graph style for
X
2T
to
ë
(path).
Tip:
Try setting the graph styles to
ë
X
1T
and
ì
X
2T
, which simulates a
chair on the ferris wheel and the ball flying through the air when you
press
s
.
Using Parametric Equations: Ferris Wheel Problem
Problem
Procedure
… 332 …


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