PARAMETRIC PROJECT
DUE DATE ____________
THE RESCUE EFFORT
Several of your friends have decided to go on a camping trip out west in a remote area. Camping is
restricted to an area 20 miles north and 30 miles east of the main lodge. Since you are a ranger at the park, you
drove your friends by jeep to an area 17 miles north of the main lodge and dropped them off at 9:00 a.m. They
have decided to hike to a remote cabin not accessible by vehicle to spend a few days camping. The group
travels 0.05 miles south and 0.1 miles east every minute.
Unfortunately, a group of convicted felons have broken out of prison and are planning to use the remote
cabin as their hide out. The outlaws began their hike to the remote cabin 30 miles east of the main lodge. They
are traveling 0.08 miles north and 0.12 miles west every minute.
You are heading up a rescue team of park rangers which has been formed to try to intercept your group of
friends before they reach the remote cabin. After receiving the bulletin, it took the rangers 45 minutes to
organize. You left by horseback from the barn which was located 2 miles north of the main lodge traveling 0.12
miles north and 0.16 miles east every minute. Will the rangers reach the trail that your friends are on in time to
tell them of the impending danger?
Part I. Organize your work neatly and briefly describe your procedure for finding the following information.
Show all of your work on a separate sheet of paper. Label all solutions.
a) Find a system of parametric equations to describe the path of each group (hikers, felons and rangers).
Show work.
b) On the same grid draw accurate graphs for each group. Be sure to label each path and the axes. If you
know how, you may use TI Connect to print the screen of your calculator.
c) Where is the remote cabin with respect to the main lodge? (Remember, the hikers and the felons are
headed directly for the cabin.) Explain your procedure for finding the solution.
d) How far will your friends have to hike to the remote cabin and how long will it take? How far will the
criminals have to hike and how long will it take them? Explain your procedure for finding the answers.
Show work.
e) Will the rangers reach the hikers in time? How long and how far will the rangers go before they reach
the hikers? Explain your procedure for finding the answers and show work.
f) What will be the most direct route to safely bring your friends back to the main lodge? How far is it?
Explain your procedure for finding the answer and show work.
Part II.
Hearing the commotion, the criminals were forewarned and escaped. Since you were the lead ranger on the
rescue mission, the FBI wants a detailed report from you on the events of the day as you know them.
Remember, the FBI will be looking for the compass headings, speed in miles/hour, distances in miles and
time of day.
Grades will be based on the following:
 Answering all questions
 Following all directions
 Showing all work
 Neatness
 Accuracy
 Overall Presentation – at a minimum your report must be typed