Texas Instruments TI-82 User Manual - Page 208

Reservoir Problem On the TI.82, parametric graphing can be used to animate a process, providing valuable insight into dynamic problems such as water flow out of a reservoir. Problem A new park has a series of waterfalls, fountains, and pools (reservoirs). The height of one of the reservoirs is 2 meters. Several holes of relatively small diameter will be drilled in the side to make streams of water that fall into the next pool. At what height on the reservoir should a hole be placed to get the maximum distance for the water jet? (Assume that the hole is at x=0, there is no acceleration in the x-direction, and there is no initial velocity in the y-direction.) Integrating the definition of acceleration in both the x and y directions twice yields the equations x=v0t and y=h0-(gà2)t2. Solving Bernoulli's equation for v0 and substituting into v0t, we get the parametric equations xt = t ‡(2 g (2 - h0)) yt = h0 - (g à 2) t2 where t is the time in seconds, h0 is the height of the hole in the reservoir in meters, and g is the acceleration of gravity (9.8 meters/sec2). Procedure 1. Press z. Select Par, Simul, and the defaults. 2. Press o and ' all functions. Enter the equations to plot the water jet for a hole at height 0.5 meters. X1T=T‡(2...9.8(2-0.50)) Y1T=0.50-(9.8à2)T2 3. Press Í to move to X2T. Press y [RCL] y [Y-VARS] 2 (to display the Parametric... menu) 1 (to select X1T) Í. This recalls the contents of X1T into X2T. Change the height from 0.50 to 0.75 meters. Repeat the process to recall Y1T into Y2T and edit it. 14-14 Applications