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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.
- Fall '07