17–12 Applications
82501F~1.DOC TI-83 international English Bob Fedorisko Revised: 10/26/05 1:49 PM Printed: 10/27/05 3:04
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 = 2pTs 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
cosq
Y(T) = Tv
0
sinq 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=L13 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
X2T to ë
ëë
ë (path).
Tip: Try setting the graph styles to ë
ëë
ë X1T and ì
ìì
ì X2T, 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
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