blueexam2sol.07f

blueexam2sol.07f - blue MATH 32A Exam 2 November 29, 2007...

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Unformatted text preview: blue MATH 32A Exam 2 November 29, 2007 LAST NAME FIRST NAME ID NO. Your TA: To receive credit, you must write your answer in the space provided . DO NOT WRITE BELOW THIS LINE 1 (25 pts) 5 (25 pts) 2 (25 pts) 6 (25 pts) 3 (25 pts) 7 (25 pts) 4 (25 pts) 8 (25 pts) TOTAL 2 PROBLEM 1 (25 Points) A miniature rocket leaves the origin at time t = 0 with initial velocity (units are meters and seconds) v = ( 40 , 40 ) m/s 2 x y The rockets acceleration vector a ( t ) has a horizontal com- ponent ( 8 , ) supplied by the rocket engines and a verti- cal component due to gravity of magnitude g m/ s 2 in the downward direction. Use the approximate value g = 10. (A) Find the rockets position r ( t ) at time t . Answer : (B) How far from the origin does the rocket land? Answer : 3 Solution: (A) We have r ( t ) = ( 8 , 10 ) . Therefore r ( t ) = t ( 8 , 10 ) + ( 40 , 40 ) We have r (0) = ( , ) since the rocket begins at the origin. Thus r ( t ) = 1 2 t 2 ( 8 , 10 ) + t ( 40 , 40 ) (B) The rockets y-coordinate is 5 t 2 +40 t = 5 t ( t 8), so the rocket lands (crashes) at time t = 8 s. The x-coordinate is x = 4 t 2 + 40 t , so the distance from the origin when the rocket lands is x (8) = 4(8 2 ) + 40(8) = 576 m 4 PROBLEM 2 (25 Points) Calculate the curvature of r ( t ) = ( t, t 1 , t 2 ) at t = 1....
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This test prep was uploaded on 04/22/2008 for the course MATH 32A taught by Professor Gangliu during the Winter '08 term at UCLA.

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blueexam2sol.07f - blue MATH 32A Exam 2 November 29, 2007...

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