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2D motion of model rocket

  1. Jan 31, 2008 #1
    1. The problem statement, all variables and given/known data

    A faulty model rocket moves in the xy-plane (the positive y-direction is vertically upward). The rocket's acceleration has components ax= [tex]\alpha[/tex]t^2 and ay=[tex]\beta[/tex]-[tex]\gamma[/tex]t , where [tex]\alpha[/tex]=2.50m/s^4, [tex]\beta[/tex]=9.00m/s^2, and [tex]\gamma[/tex]=1.40m/s^3. At t=0 the rocket is at the origin and has velocity [tex]\overline{v0}[/tex] = v0x[tex]\widehat{i}[/tex] + v0y[tex]\widehat{j}[/tex]with v0x = 1m/s and v0y = 7m/s.

    question: what is the rockets' maximum height reached?

    2. Relevant equations

    1. [tex]\overline{v}[/tex](t) = v0x + [tex]\alpha[/tex]t^3/3, v0y + ([tex]\beta[/tex]t-[tex]\gamma[/tex]t^2/2)

    2. [tex]\overline{r}[/tex](t) = v0xt + [tex]\alpha[/tex]t^4/12, v0yt + ([tex]\beta[/tex]t^2/2 - [tex]\gamma[/tex]t^3/6)

    other equations I tried, might help

    3. x = (v0cos[tex]\alpha[/tex]0)t

    4. y = (v0sin[tex]\alpha[/tex]0)t-1/2gt^2

    5. vx = v0cos[tex]\alpha[/tex]0

    6. vy = v0sin[tex]\alpha[/tex]0-gt

    7. y-y0 = v0yt+1/2gt^2

    8. quadratic equation -b = +/- [tex]\sqrt{b^2-4ac}[/tex]/2a

    3. The attempt at a solution

    this is a masteringphysics problem in which I was supposed to originally find the velocity and position vectors which easily enough I found to be the integral of the acceleration and the integral of velocity respectively.

    I originally tried using the quadratic equation with the components of the y component of equation 2 to solve for time and plug that time back into the y component of the position vector and solve for y.

    problem was I kept on getting very tiny numbers and eventually I ran out of attempts and the masteringphysics system just gave the answer to be 341m, I have no idea how they did that with the info presented, if anyone could give me any hints as to how the question is done that would be very helpful.
  2. jcsd
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