yellowexam2sol.08w

yellowexam2sol.08w - yellow MATH 32A Exam 2 LAST NAME FIRST...

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yellow MATH 32A Exam 2 February 20, 2008 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 (20 pts) 5 (20 pts) 2 (10 pts) 6 (20 pts) 3 (20 pts) 7 (20 pts) 4 (20 pts) TOTAL
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2 PROBLEM 1 (20 Points) State and prove Kepler’s Second Law of Planetary Motion. To do this, you will have to include a statement of Newton’s Second Law of Motion and Universal Law of Gravitation and show how they are used. Solution: See text.
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3 PROBLEM 2 (20 Points) A particle travels along the curve y = x 3 . Assume units of meters and seconds. At a certain moment, the particle is located at the point P = (1 , 1) and at this moment, the particle’s acceleration vector is a = h- 60 , 60 i How fast is the particle moving at this moment? Answer :
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4 Solution: Using the parametrization r ( t ) = h t,t 3 i , we have r 0 ( t ) = h 1 , 3 t 2 i . The unit tangent vector at t = 1 is T = h 1 , 3 i 10 and therefore the unit normal (which points in the direction of curvature) is N = h- 3 , 1 i 10 The normal component is
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yellowexam2sol.08w - yellow MATH 32A Exam 2 LAST NAME FIRST...

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