1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Vector functions help

  1. Oct 8, 2004 #1
    i need a little help with this problem, i can get most of it set up but there is one part where i get stuck heres the question.

    You are the captin of a spaceship that has been given the mission of flying from a spacestation at position (1,2,3) to a spacestation at position (4,7,5) in one hour, both departing and arriving with 0 velocity, and arriving with 0 acceleration. You are able to fire the engines so that the accereration of the spaceship is at time t (measured in hours after the departure) is given by the formula : a(t) = t^2b + tc +d for any choice of the constant vectors b,c and d. Determine choices of these constant vectors so that you can complete your mission.

    so far this is what i have:

    a(0)= d
    a(1)= b+c+d = 0

    v(t)= (1/3)*t^3*b + (1/2)*t^2*c +d*t +k_1
    v(0)=0+k_1 so k_1=0
    v(1)= (1/3)*b + (1/2)*c + d = 0

    r(t)= (1/12)*t^4*b + (1/6)*t^3*c + (1/2)*t^2*d +k_2
    r(0)= 0+ k_2 so k_2 = (1,2,3)
    r(1)= (1/12)*b + (1/6)*c + (1/2)*d +(1,2,3) = (4,7,5)

    i then tried to solve them in a linear system using t=1, since i have 3 variables and 3 equations, but im not sure how i would handle the r(1) situation since i have two points in the equation, and the rest are vectors.

    can anyone help me out here?

  2. jcsd
  3. Oct 8, 2004 #2
    actually you have
    a(1) = b+c+d = (0,0,0)
    v(1) = (1/3)b + (1/2)c +d = (0,0,0)
    r(1) = (1/12)b + (1/6)c + (1/2)d + (1,2,3) = (4,7,5)

    That´s because velocity and acceleration are also vectors, not scalars. You can either solve these equations for b,c,d like you´d do for real numbers (well, as long as you only add them or multiply them with real numbers, but that´s sufficient) or, if you feel uncomfortable doing that, break up these equation by b=(bx,by,bz), c=(cx,cy,cz), d=(dx,dy,dz) into a system of 9 equations with 9 unknowns (not recommended).

    If your problem is that P0=(1,2,3) and P1=(4,7,5) are points in space while a,b,c are vectors and you are afraid of mixing points and vectors then remember that the difference P1-P0 = r(1)-r(0) = (4,7,5)-(1,2,3) between start- and endpoint is a vector.

    Hope that helps.

    Sidenote: Thumbs up that you presented your work on the problem - and even in a very readable form. That´s seen way too seldom when people ask for homework help.
    Last edited: Oct 8, 2004
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook