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TI-83 Plus Activities 580
Using Parametric Equations: Ferris Wheel
Problem
Problem
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
= 2
p
Ts 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
cos
q
Y(T) = Tv
0
sin
q
N
(g
à
2) T
2
where g = 9.8 m/sec
2
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