Using Parametric Equations: Ferris Wheel Problem - Texas Instruments TI-82 STATS Manual Book

Using Parametric Equations: Ferris Wheel Problem

Problem
Procedure
17–12 Applications
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
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 ) of 22 meters per second at an angle (q) of 66¡ from
0
the horizontal. The parametric equations below describe the
location of the ball at time T.
X(T) = b N Tv cosq
0
Y(T) = Tv sinq N (g à 2 ) T
0
2
9.8 m / sec
1. Press z. Select
(simultaneous) mode simulates the two objects in
Simul
motion over time.
2. Press p. Set the viewing window.
Tmin=0
Tmax=12
Tstep=.1
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
Tip: Try setting the graph styles to
a chair on the ferris wheel and the ball flying through the air when you
press s.
where a = 2pTs and r = d à 2
2
, , and the default settings.
Par Simul
Xmin=L13
Xmax=34
Xscl=10
ë ë ë ë
to
X
2T
ë ë ë ë X
and
1T
where g =
Ymin=0
Ymax=31
Yscl=10
(path).
ì ì ì ì X
, which simulates
2T