Final fall 2014 solutions - Northwestern University Math...

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Northwestern University Math 230 Final exam December 10, 2014 Last name . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . First name . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Email . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . NetID . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Student ID . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Instructions: This exam has 15 problems and 17 pages. Please make sure that all pages are in- cluded. Read each problem carefully. Write legibly. Cross off anything you do not wish graded. Write in complete sentences. You may not use books, notes, calculators or phones. You have 120 minutes to complete this exam. DO NOT write outside of the box on each page. Good luck!
Problem 2 (18 points) A Frontier airplane follows the path F ( t ) = h 3 - t , 1 + t , 3 t i and a Southwest airplane follows the path S ( t ) = h 6 - t , - 1, - 3 - 3 t i . An observer on the ground notices that the lines of steam emitted from the planes appear to cross. Do they actually cross, and if so, at what point?
(4 pts for realizing that they need to solve a system of equations)

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