Exam 1 - APPM 2350 EXAM 1 FALL 2010 INSTRUCTIONS:...

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APPM 2350 EXAM 1 FALL 2010 INSTRUCTIONS: Electronic devices are not permitted during the exam. Write your name, your instructor’s name, and your recitation number on the front of your bluebook. Start each problem on a new right-hand page. Justify your work clearly and box your Fnal answer. A correct answer with incorrect or no supporting work may receive no credit, while an incorrect answer with relevant work may receive partial credit. 1. (25 points) Consider a particle moving along a path r ( t ) such that its speed is always 37, the curvature is always 1 / 37, the acceleration is a ( t )= cos( t ) i +0 j sin( t ) k , and the unit tangent to the path is T ( t )= (1 / 37)( sin( t ) i +6 j + cos( t ) k ). (a) Calculate the velocity, V ( t ). (b) Calculate the unit normal to the path, N ( t ). (c) Calculate the unit binormal to the path, B ( t ). (d) At time t ° =2 π the particle is located at (1 , 12 π, 0). Determine r ( t ). (e) Determine the constants a , b , and c , if one were to write the position vector at time t ° in the form r ( t ° )= a T ( t ° )+ b N ( t ° )+ c B ( t ° ). 2. (25 points) Suppose a probe is launched into deep space at time t = 0 from its mother ship to search for other lifeforms that understand vector calculus. The probe travels along with velocity
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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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Exam 1 - APPM 2350 EXAM 1 FALL 2010 INSTRUCTIONS:...

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