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Kinematics and finding acceleration

  1. Oct 2, 2013 #1
    1. The problem statement, all variables and given/known data

    A weather rocket is launched straight upwards. The motor provides a constant acceleration for
    18s, then the motor stops. The rocket altitude after 26s after launch is 5800m. What was the rocket's acceleration during the first 18 seconds?

    2. Relevant equations
    [ tex ]x = x_0 + v_0 t + (1/2) a t^2
    [/tex]
    [ tex]v = v_0 + a t
    [/tex]


    3. The attempt at a solution
    This answer doesn't seem right to me. I wasn't confident working it out.

    5800=.5(a)(18)^2-(.5)(9.81)(8)^2
    162a=5800+313.92
    162a=6113.92
    a=37.7
     
  2. jcsd
  3. Oct 2, 2013 #2

    PhanthomJay

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    You forgot to include the initial velocity of the rocket during the second part of the trip with the motor stopped.
     
  4. Oct 3, 2013 #3
    I don't know the velocity at 18 seconds. All the initial values are given, they are all zero. The only intermediate value given is 18 seconds. That's why I'm having a difficult time, I'm not sure how to handle all the unknowns. I'm trying to draw some equations from the three graphs I drew but some of the equations don't make sense. Thank you for your reply.
     
  5. Oct 3, 2013 #4

    PhanthomJay

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    you can use your 2nd relevant equation , where v in that equation after 18 s becomes v_o in your first relevant equation . You will have to leave a as unknown, then solve.
     
  6. Oct 3, 2013 #5

    HallsofIvy

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    Let the "constant acceleration" while the rocket engine is firing be "a". Then the height when the engine stops firing, from s= (a/2)t^2, is (a/2)(18)^2= 162a meters and its speed is 18a meters per second. After that, we have only the acceleration due to gravity: h= 162a+ 18a(t- 18)- 4.9(t- 18)^2. (Do you see why "t- 18"?) Set t= 26 s, h= 5800 m and solve for a.
     
  7. Oct 3, 2013 #6
    Thanks for both your help guys. I've been doing physics for all of three weeks now and it doesn't seem to be getting easier. Sorry for the messy equations. I tried to use latex but apparently it didn't work. Thanks again!
     
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