17----blueexam2sol[1]

17----blueexam2sol[1] - blue MATH 32A Exam 2 LASTNAME FIRST...

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Sheet1 Page 1 blue MATH 32A Exam 2 November 29, 2007 LASTNAME FIRST NAME IDNO. YourTA: 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
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Sheet1 Page 2 PROBLEM 1 (25 Points) A miniature rocket leaves the origin at time t = 0 with initial velocity(units are meters and seconds) 2 v0 Err:509 xy onent h8,0i supplied by the rocket engines and a verti 2 cal component due to gravity of magnitude g m/sin the downward direction. Use the approximate value g =10. Answer: (B)How far from the origin does the rocket land? Answer: A ' (t) Solution: (A)We have r Err:509 r (t)= th8,-10i+ h40,40i We have r(0)= h0,0i since the rocket begins at the origin. Thus r(t)= 1 t2h8,-10i+ th40,40i 2 The rockeths acceleration vector a(t)has a horizontal comp (A)Find the rockethsposition r(t)at time t. (B)The rockethsy-coordinateis -5t2
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Sheet1 Page 3 +40t = -5t(t-8), so the rocketlands(crashes) attime t =8s. Thex-coordinate is x =4t2 +40t, so the distance from the origin when the rocket lands is x(8)=4(82)+40(8)=576 m x PROBLEM 2 (25 Points) Calculate the curvature of r(t)= ht,t-1,t2i at t =1.
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