Operation Manual

Chapter 17: Activities 316
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.
4. Press s to graph the equations. Watch closely as they are plotted. Notice that the ball and the
ferris wheel passenger appear to be closest where the paths cross in the top-right quadrant of the
ferris wheel.
5. Press p. Change the viewing window to concentrate on this portion of the graph.
6. Press r. After the graph is plotted, press ~ to move near the point on the ferris wheel where
the paths cross. Notice the values of
X, Y, and T.
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
Tst e p=. 1
Xmin=
L13
Xmax=34
Xscl=10
Ymin=0
Ymax=31
Yscl=10
Tmin=1
Tmax=3
Tst e p=. 0 3
Xmin=0
Xmax=23.5
Xscl=10
Ymin=10
Ymax=25.5
Yscl=10