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Unformatted text preview: MATH 317 T2 SOLUTIONS TO MIDTERM #1 1. As shown in class, the curvature .  ) (   ) ( ) (  ) ( 3 t t t t r r r = In this question . ) ( ) ( ) ( , ) ( ) ( ) ( ) ( ) ( ) ( j i r j i r j i r t g t f t t g t f t t g t f t + = + = + = Hence  ) ( ) ( ) ( ) (   ) ( ) (  . t f t g t g t f t t  = r r and 2 2 )] ( [ )] ( [  ) (  . t g t f t + = r . In turn this yields the given answer. 2. (a) The velocity is given by , 2 ) ( ) ( k j i r v + = = t t e e t t the acceleration by . ) ( ) ( ) ( j i r v a t t e e t t t + = = = (b) The unit tangent vector to the path is given by = =  ) (  ) ( t t r r T . 2 2 2 2 + + + t t t t e e e e k j i (c) The length of the path is given by . ) ( ) ( 2  ) (  1 1 1 2 1 2 2 1 = + = + = + + = e e dt e e dt e e dt e e dt t t t t t t t r (d) The curvature of the path at time t is given by ....
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This note was uploaded on 04/01/2010 for the course MATH 317 MATH 317 taught by Professor Bluman during the Spring '10 term at The University of British Columbia.
 Spring '10
 BLUMAN

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