Operation Manual

14-12 Applications
8214APPS.DOC TI-82, Chapter 14, English Bob Fedorisko Revised: 02/09/01 9:27 AM Printed:
02/09/01 12:43 PM Page 12 of 20
Ferris Wheel Problem
Use two pairs of parametric equations to describe two objects in motion, a
person on a ferris wheel and a ball thrown to that person. Determine when the
two objects are closest.
Problem
The ferris wheel has a diameter of 20 meters (d) and is rotating
counterclockwise at a rate of one revolution every 12 seconds (s). The
following parametric equation describes the location of the person on the
ferris wheel at time T, where
a
is the angle of rotation, the bottom center of
the ferris wheel is (0,0), and the passenger is at the rightmost point (10,10)
when T = 0.
X(T) = r cos
a
where
a
= 2
p
T
à
s and r = d
à
2
Y(T) = r + r sin
a
The ball is thrown from a height even with the bottom of the ferris wheel,
but 25 meters (b) to the right of the bottom center of the ferris wheel (25,0),
with velocity (v
0
) of 22 meters per second at an angle (
q
) of 66
¡
from the
horizontal. The following parametric equation describes the location of the
ball at time T.
X(T) = b – T v
0
cos
q
Y(T) = T v
0
sin
q
– (g
à
2) T
2
(g = 9.8 m/sec
2
)
Solution
1. Press
z
. Select
Par
,
Connected
, and
Simul
. Simultaneous
MODE
simulates what is happening with the two objects in motion over time.
2. Press
o
and turn off all functions. Press
y
[
STAT PLOT
] and turn off
all stat plots.
3. Press
p
. Set the viewing
WINDOW
.
Tmin = 0 Xmin =
M
13 Ymin = 0
Tmax = 12 Xmax = 34 Ymax = 31
Tstep = .1 Xscl = 10 Yscl = 10
4. Press
o
. Enter the expressions to define the path of the ferris wheel
and the path of the ball.
X
1T
= 10cos (
p
T
à
6)
Y
1T
= 10+10sin (
p
T
à
6)
X
2T
= 25–22Tcos 66
¡
Y
2T
= 22Tsin 66
¡
–(9.8
à
2)T
2