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Activities 69
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.
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.
Procedure
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.
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 (path).
Note: Try setting the graph styles to ë X1T and ì X2T, which
simulates a chair on the ferris wheel and the ball flying through the
air when you press s.
X(T) = r cos a
Y(T) = r + r sin a
where a = 2pTs and r = dà2
X(T) = b N Tv
0
cosq
Y(T) = Tv
0
sinq N (gà2) T
2
where g = 9.8 m/sec
2
Tmin=0
Tmax=12
Tstep=.1
Xmin=
L13
Xmax=34
Xscl=10
Ymin=0
Ymax=31
Yscl=10