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March 28, 2017

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A 2000 kg space probe is moving rightward in empty space along the x axis at 12 m/s. One of the probe’s rockets is fired providing a thrust of 1800j N along the y axis. The rocket fires for 1.5 s.
How can I derive the equation for the trajectory of the probe during the time the rocket is fired using the formula y = a function of x and compute the final speed of the rocket at the end of the 1.5 s?

  • physics - ,

    Thrust is in force units. For all intents and purposes, there is a force in the y-direction of 1800 N for 1.5 seconds.

    The motions in the x- and y-directions being linearly independent, we can process them separately and relate the motion using the parameter t=time.

    vx(t)=12 m/s (constant)
    force in y-direction, F = 1800 N
    mass, m = 2000 kg
    Since Force F=ma, where a = acceleration
    acceleration=F/m=1800/2000 m/s²
    =0.9 m/s²
    Initial velocity in the y-direction = 0
    therefore
    vy(t)=0+at=0.9t (0≤t≤1.5)

    The trajectory is given by the parametric formulae vx(t) and vy(t) in terms of time, t.

    The speed at any time t within the firing period (1.5 s) can be obtained by the vectorial sum of the two velocities, vx(t) and vy(t):

    Speed for 0≤t≤1.5
    S(t)=sqrt(vx(t)²+vy(t)²)
    =sqrt(12²+(0.9t)²)

    Speed at the end of the rocket firing period
    =S(1.5)

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