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Vector problem, someone please help

  1. Mar 8, 2008 #1
    A particle moves in the xy-plane so that the position of the particle is given by
    x(t)=5t+3sint , y(t)=(8-t)(1-cost)

    Find the velocity vector at the time when the particle's horizontal position is x=25
    answer is (7.008, -2.228)

    *the x=25, i think the trick is somehow get the t with that..
  2. jcsd
  3. Mar 8, 2008 #2


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    Staff Emeritus
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    Yes, it is. You have to solve 5t+ 2sin(t)= 25. There is no "algebraic" way to solve an equation like that. You will have to do it numerically. If you have a graphing calculator, you could see where the graphs of y= 5t+ 2sin(t) crosses the graph of y= 25.

    If not, you might use a "bisection" method. For example, It is obvious that X(4)= 20+ 3sin(4)< 25. It is not so obvious but easy to show with a calculator that X(7)= 28+ 3 sin(7)> 25 (but not 5 or 6). The function must be equal to 25 some place between them. Just because it is simplest, try half way between them, 5.5. X(5.5)= 25.3> 25. Now we know the function is equal to 25 some place between 4 and 5.5. Again, try half way: (4+ 5.5)/2= 4.75. X(4.75)= 20.817< 25 so now we know the solution is somewhere between 4.75 and 5.5. Half way between them is (4.75+ 5.5)/2= 5.125.

    Continue unfil you feel you have sufficient accuracy.
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