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Vector Valued Function Spaceship Problem

  1. Jan 28, 2013 #1
    1. The problem statement, all variables and given/known data

    The position function of a spaceship is r(t)= < 3+T, 2+ln(T), 7 -(4/T2+1)> , and the coordinates of a space station are (6, 4, 9). The captain wants to coast into the space station. When should the engines be turned off?

    2. Relevant equations
    I took the derivative of the position function to get the velocity function:
    V(t)= <1, (1/T), (8T)/(T2+1)2


    3. The attempt at a solution

    Right now I have a vector I called U =<6-3+s>, 4 -(2+ln(s)), 9-[7-(4/s2+1)]
    I got this hint from my professor. I understand that this is the position vector to the spaceship at time s. I know I now need to find the velocity vector that is parallel to the position vector. My professor gave me the hint to multiply by a constant K in the velocity vector function. At that point I would have two equations, and two unknowns which is easy to solve. I am just stuck on when I multiply by the constant K what would I set the velocity vector function equal too?
     
  2. jcsd
  3. Jan 28, 2013 #2
    When the engines are switched off, the spaceship will probably move in a straight line. So you want to switch them off when your velocity vector points from r(t) towards the space station.
     
  4. Jan 28, 2013 #3

    LCKurtz

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