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Maximum height of a toy rocket?

  1. Sep 25, 2011 #1
    maximum height of a toy rocket??

    1. The problem statement, all variables and given/known data
    A toy rocket is launched vertically from ground level(y=0) at time t=0s. The rocket engine provides constant upward acceleration during the burn phase. At the instant of engine burnout, the rocket has risen to 49 m and aquired a velocity of 60m/s. The rocket continues to rise in unpowered flight, reaches maximum height, and falls back to the ground. The maximum height reached by the rocket is closest to
    A. 244m
    B. 256m-wrong
    C. 221m
    D. 233m
    E. 209m


    2. Relevant equations

    y=vy*t+1/2g*(t^2)

    3. The attempt at a solution
    0= 60m/s*t+4.9m/s^2(t^2)
    yaya not sure what i just did.
     
  2. jcsd
  3. Sep 25, 2011 #2

    PhanthomJay

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    Re: maximum height of a toy rocket??

    Try another of the kinematic eqautions, knowing that when the rocket reaches the top of its flight, its motion comes to a temporary stop.
     
  4. Sep 25, 2011 #3
    Re: maximum height of a toy rocket??

    would it be something like vf^2=v0^2+2g(change in)y ??
     
  5. Sep 25, 2011 #4

    I like Serena

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    Re: maximum height of a toy rocket??

    Close! :smile:
    Actually vf^2=v0^2-2g(change in)y
    since the acceleration is -g.
     
  6. Sep 25, 2011 #5
    Re: maximum height of a toy rocket??

    okay but now i forgot what i need to plug in where. i know vf is 60 and i know g but am i looking for y or v0?
     
  7. Sep 25, 2011 #6
    Re: maximum height of a toy rocket??

    I would solve it by finding how high the rocket went with the constant acceleration and then the velocity at the time that the acceleration stops. Then I would put the final velocity as the initial velocity for the second equation of displacement formula. Take the derivative of that and solve for time when the velocity is zero (at its highest point). Then I would think about what left I have to do to solve for the total displacement traveled at its highest point.
     
  8. Sep 25, 2011 #7
    Re: maximum height of a toy rocket??

    okay you just lost me. too much at once.
     
  9. Sep 25, 2011 #8

    I like Serena

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    Re: maximum height of a toy rocket??

    You need to split the trajectory into separate parts.
    First part is when the engine is burning.
    The problem states it gets up to a height of 49 meters, and at that point it has a velocity of 60 m/s.

    Then you get the second part of the trajectory where you need to use the formula.
    At that time the "initial velocity" is 60, and the trajectory continues until the rocket is at its highest point.
    What is the "change in y" for this second part of the trajectory?
     
  10. Sep 25, 2011 #9
    Re: maximum height of a toy rocket??

    uhh 3619.6m
     
  11. Sep 25, 2011 #10

    I like Serena

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    Re: maximum height of a toy rocket??

    Uhh :uhh:
    How did you get that? :confused:
    Can you show your calculation?
     
  12. Sep 25, 2011 #11
    Re: maximum height of a toy rocket??

    The answer I got was closest to D. 233m. That is correct in your textbook?
     
  13. Sep 25, 2011 #12
    Re: maximum height of a toy rocket??

    umm i did 60^2 + (9.8*2)
     
  14. Sep 25, 2011 #13
    Re: maximum height of a toy rocket??

    this text book doesnt have answers. how did you get that??
     
  15. Sep 25, 2011 #14
    Re: maximum height of a toy rocket??

    I am not sure if I can show the step-by-step mathematics here to give you the answer. It involves basic calculus and rearranging the formulas of the the position function. A major hint is this equation:

    Let up be positive:

    x(t) = -1/2gt^2 + 60t, where g = 9.8 m/s/s
     
  16. Sep 25, 2011 #15

    I like Serena

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    Re: maximum height of a toy rocket??

    I'm afraid that is not right.

    Your formula is:
    [tex]v_f^2=v_0^2-2g\Delta y[/tex]
    To find (change in)y, you'd have:
    [tex]\Delta y = {v_0^2 - v_f^2 \over 2g}[/tex]
     
  17. Sep 25, 2011 #16
    Re: maximum height of a toy rocket??

    yeah i figured it wasn't. i followed the formula you just game me and i came up with change in y= 2.5m is this right?
     
  18. Sep 25, 2011 #17
    Re: maximum height of a toy rocket??

    What person are you talking to? :tongue:
     
  19. Sep 25, 2011 #18
    Re: maximum height of a toy rocket??

    i was talking to i like serena, his equation was easier to figure out than yours was.
     
  20. Sep 25, 2011 #19

    I like Serena

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    Re: maximum height of a toy rocket??

    Noooooooo. :wink:

    Try:
    [tex]\Delta y = {v_0^2 - v_f^2 \over 2g} = {60^2 - 0^2 \over 2 \cdot 9.8}[/tex]
     
  21. Sep 25, 2011 #20
    Re: maximum height of a toy rocket??

    My equation is the position traveled when gravity takes over. It is simplified to x(t) = -4.9t^2 + 60t
     
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