13.3-13.4soln

13.3-13.4soln - MATH 231 Group Work Quiz Related 1. Compute...

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MATH 231 Group Work Quiz Related 1. Compute T ( t ), N ( t ), B ( t ) and κ ( t ) for the following curves: (a) r ( t ) = t 3 j - 4 t k (b) r ( t ) = 1 2 sin t i + 1 2 cos t j + 1 2 t k Answers: (a) There was a terribly cruel typo on this problem which makes doing this extremely ugly. The problem should read r ( t ) = t 3 j - 4 k . With that, it makes the problem substantially easier. Then T ( t ) = h 0 , 1 , 0 i , N ( t ) = h 0 , 0 , 0 i , B ( t ) = h 0 , 0 , 0 i , and κ ( t ) = 0. (b) T ( t ) = 2 h cos t, - sin t, 1 i , N ( t ) = h- sin t, - cos t, 0 i , B ( t ) = ± cos t, - sin t, - 2 ² , and κ ( t ) = 4. 2. A gun is fired with angle of elevation 30 . What is the muzzle speed if the maximum height of a shell is 500 m? Answer: We have two equations: y = v 0 sin( α ) t - 9 . 8 2 t 2 , y 0 = v 0 sin α - 9 . 8 t We know that, at the maximum height, y = 500 and y 0 = 0, so we have two equations with two unknowns (seeing as α = 30 ). Solving these equations for v 0 , we find that v 0 198 m/s. 3. At what point does the curve have maximum curvature?
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13.3-13.4soln - MATH 231 Group Work Quiz Related 1. Compute...

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