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!

Deriving Rocket's position from acceleration.

  1. Dec 9, 2012 #1
    1. The problem statement, all variables and given/known data
    There's a short introduction saying that honing missiles can determine their position by utilizing their acceleration, then the problem says: Suppose that the missile's acceleration obeys the following equations:
    [tex]
    \\
    a_x = 0.8\\
    a_y = -6.0 - 3.0t
    [/tex]
    Knowing that, in [itex]t = 0[/itex], [itex]v_x = 600 km/h[/itex] and [itex]v_y = 0[/itex], calculate the missile's displacement in ten seconds. (Answer is 2.2km)

    2. Relevant equations

    Just the equations already provided.

    3. The attempt at a solution
    Alright, so, what I tried to do was integrating the acceleration two consecutive times to arrive at an equation for x(t) and y(t), which gave me:
    [tex]
    \\
    x(t) = 0.4 t^2 + 600t + x_o\\
    y(t) = \frac{-1}{2}t^3 - 3t^2 + y_0
    [/tex]

    Then I attempted to get the displacement of both axes(Using time = 1/360h, since I have to convert 10 seconds to hours):
    [tex]
    \\
    x(10)-x(0) = 1.67km\\
    y(10)-y(0) = -2.3*10^{-5} km
    [/tex]
    And then, by calculating[itex]sqrt(x^2 + y^2) [/itex]I obviously get pretty much 1.67km, which is wrong.
     
  2. jcsd
  3. Dec 9, 2012 #2

    haruspex

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    2016 Award

    What are the units of distance and time in those equations?
     
  4. Dec 10, 2012 #3
    That's a great question. I just realized it says in parenthesis (SI Units), so m/s. In other words, I shouldn't convert time to seconds, I should convert km/h to m/s. However, by converting 600 km/h to 166.67 m/s and doing the necessary calculations I still obtain only 1884.26 m(With x =1706 and y = -800) : S
     
  5. Dec 10, 2012 #4

    haruspex

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    2016 Award

    ax = 0.8 looks suspicious. Why so much less than ay? If you make it 8.0 you get the book answer.
     
  6. Dec 10, 2012 #5
    Wow, you're absolutely right! Wonderful! Thanks.

    It definitely says 0.8 and It's actually an online list of exercises, not a textbook, so I find very possible that the person that typed it made a mistake.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Deriving Rocket's position from acceleration.
Loading...