Homework 3 Solutions

Homework 3 Solutions - HOMEWORK 03 Solutions(1 Suggested...

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HOMEWORK 03 Solutions (1) Suggested Problems (2) Suggested Problems (3) Calvin the ant has recently found some spilled beer on a college campus. The location of the spill is (1 , 2 , 0). He wishes to return to his anthill to report on the Fnd, however, for some reason, he Fnds that instead of walking in a straight path, he returns home along a path that has velocity v ( t )=(cos t +1) i +5 j +0 k starting at time t =0 . (a) What is Calvin’s actual path r ( t )? r ( t )= ° v ( t ) dt =(s in t + t + c 1 ) i +(5 t + c 2 ) j + c 3 k .T os o l v ef o r c 1 ,c 2 , and c 3 we use his postion at t =0 . r (0) = c 1 i + c 2 j + c 3 k = i +2 j +0 k r ( t )=(s in t + t +1) i +(5 t +2) j +0 k (b) If the entrance to the anthill is at ( 3 π 2 , 15 π +4 2 , 0), will Calvin make it to the entrance? If so, when? To make it to the entrance, there must be some value t 0 for which r ( t 0 )= 3 π 2 i + 15 π +4 2 j +0 k .Th i sg iv e su sth re eequa t ion s : sin t 0 + t 0 +1 = 3 π 2 5 t 0 +2 = 15 π +4 2
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Homework 3 Solutions - HOMEWORK 03 Solutions(1 Suggested...

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