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Homework Help: Rocket velocity/displacement problem, HELP

  1. Sep 21, 2009 #1
    1. The problem statement, all variables and given/known data
    A two stage rocket is launched with an average acceleration of +4 m/s/s. After 10 seconds, a second stage is activated and the rocket's acceration is now +6 m/s/s.

    Part A: Find the vertical displacement of stage one of the rocket, before accleration changes to 6.

    Part B: Find the final speed after 10 seconds of motion.

    Part C: The second stage is activated, find the total height the rocket ascends (its highest point) before it starts to travel back to earth.

    Part D: Find the displacement traveled by the second stage only.

    2. Relevant equations
    Vf = Vi + a[tex]\Delta[/tex]t

    [tex]\Delta[/tex]y = Vi[tex]\Delta[/tex]t + 0.5a([tex]\Delta[/tex]t)^2

    (Vf)^2 = (Vi)^2 + 2a[tex]\Delta[/tex]y

    3. The attempt at a solution

    For Part A I calculated displacement with [tex]\Delta[/tex]y = Vi[tex]\Delta[/tex]t + 0.5a([tex]\Delta[/tex]t)^2.
    y was my unknown variable and my Vi was 0, my t 10 seconds, and my a +4.
    I got 200meters.

    For Part B I calculated the first stage's final speed by using the equation Vf = Vi + a[tex]\Delta[/tex]t.

    I had a Vi of 0, an accleration of +4 and a t of 10. My velocity final was +40 m/s.

    As far as part c goes I plugged everything into
    (Vf)^2 = (Vi)^2 + 2a[tex]\Delta[/tex]y
    this time I had a velocity initial as +40 [part b] and i used 0 as my velocity final because i was solving for the peak. However, my negative signs got messed up. Here's where I need help. Am I on the right track??
  2. jcsd
  3. Sep 21, 2009 #2
    you need to know how long the second stage burns. When the second stage burns
    a = 6 m/s^-2 and you can compute the final speed and height as you did in part A and B.
    After the second stage stops burning the rocket is in freefall, but it will still move up for some time and you can use [itex] {V_f}^2 = {V_i}^2 + 2a \Delta y [/itex]
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