Precalculus: Chapter 6 – Parametric Equations
Name _____________________________
Two cars are in a 500 mile race. One car averages 105 mph and the other averages 120 mph but is delayed
30 minutes at the start of the race due to electrical problems. Which of the two cars will finish first,
assuming they both finish the race? First, you must write a pair of parametric equations to represent each
car’s position after t hours. Place car one in track 1 and car two in track 2. Determine the appropriate x, y,
and t range values in order to view the graph.
How far behind is the car that finished 2nd?
A third car races at an average of 110 mph and is only delayed 20 minutes at the start of the race. Now who
wins?
How far behind are the other 2 cars?
Which car will finish second?
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Two opposing players in “Capture the Flag” are 100 feet apart. On a signal, they run to capture a flag that is
on the ground midway between them. The faster runner, however, hesitates for 0.1 sec. The following
parametric equations model the race to the flag:
x1  10  t  0.1 , y1  3
x2  100  9t ,
y2  3
Describe the meaning of these two equations.
Simulate the game in a [0,100] by [-1,10] viewing window with t starting at 0. Graph simultaneously.
Who captures the flag?
By how many feet?
The winner, feeling confident, tells the opposing player that he/she will hesitate for 0.5 seconds this time.
This of course changes the equation for the winner. What would the new equation be?
Does this guarantee a win for the opposing player? Prove this algebraically.
Keeping the last question in mind, how much of a head start could the winner give before the opposing
player actually wins the race?
If a new challenger with a rate of 9.5 plays the winner (who is still feeling confident and hesitates for 0.5
seconds), who is the winner now and by how many feet?