Homework 3 - t = 0 to t = 3 π 2 ? (d) How far would Calvin...

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APPM 2350 HOMEWORK 03 FALL 2010 Due by 4 PM on Friday, September, 17, 2010 in your TA’s mailbox 1. Work all of the “suggested” textbook problems. Remember that you do not need to write them up or submit them. Just be sure you can do, and understand, all of them prior to starting the homework problems that you submit for grading. 2. If you have not ±nished problem 1, go back and ±nish it. 3. Calvin the ant has recently found some spilled beer on a college campus. The location of the spill is (1 , 2 , 0). He wishes to return to his anthill to report on the ±nd, however, for some reason, he ±nds that instead of walking in a straight path, he returns home along a path that has velocity v ( t ) = (cos( t ) + 1) i +5 j +0 k starting at time t = 0. (a) What is Calvin’s actual path r ( t )? (b) If the entrance to the anthill is at ° 3 2 π, 15 π +4 2 , 0 ± , will Calvin make it to the entrance? If so, when? (c) How far would Calvin walk from
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Unformatted text preview: t = 0 to t = 3 π 2 ? (d) How far would Calvin walk if he went directly from the spill location to the anthill entrance? 4. Kate’s mother puts her on an amusement park ride. While on the ride, Kate follows the path r ( t ) = ( t − sin( t )) i + (1 − cos( t )) j + 0 k for 0 ≤ t ≤ 2 π . Kate’s mother stands at location (2 π, 4 , 0) while Kate is on the ride. Kate is a little scared, so she hangs on tight and stares straight ahead until the ride ends. (a) When, if ever (and at what location), does Kate stare straight at her mother while on the ride? (b) Calculate the arc length of Kate’s ride as a function of time. How far does Kate travel on the ride? (c) Using your arc length formula from part (b), how far would Kate go if she stayed on the ride for 0 ≤ t ≤ 4 π ? Comment on your results....
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This note was uploaded on 02/10/2011 for the course APPM 2350 taught by Professor Adamnorris during the Fall '07 term at Colorado.

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