Texas Instruments TI-84 PLUS SILV Guidebook - Page 324

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 Y(T) = r + r sin a where a = 2pTs and r = dà2 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 (v0) 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 Tv0 cosq Y(T) = Tv0 sinq N (gà2) T2 where g = 9.8 m/sec2 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. Tmin=0 Tmax=12 Tstep=.1 Xmin=L13 Xmax=34 Xscl=10 Ymin=0 Ymax=31 Yscl=10 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. Chapter 17: Activities 317