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Calculating impact velocity of freefalling object with increasing grav

  1. Oct 21, 2013 #1
    1. The problem statement, all variables and given/known data
    A space ship is in a vertical free fall towards an airless moon. It starts out at 1,247,000m above sea level and has an initial vertical speed of -132 m/s. The moon's radius is 200,000m and gravity at sea level is 1.63 M/s^2, but decreases with distance. Calculate the vertical velocity the ship will have by the time it impacts the moon.



    2. Relevant equations
    t=(vf-vi)/a

    t=time
    vf = velocity final
    vi = velocity initial
    a = acceleration


    d=(1/2)at^2

    d = distance


    g1=g0/((r1/r0)^2)

    g1 = initial altitude gravity
    g0 = sea level gravity
    r1 = initial altitude radius
    r0 = sea level radius


    3. The attempt at a solution

    t0 = 0
    v0 = 132
    h0 = 1217000
    a0 = 0.0311

    t1 = t0+1
    v1 = v0+a0
    h1 = h0-v0
    a1 = g0/(v1/r0)^2

    final velocity with constant lowest gravity

    vg1=278.68m/s=SQRT(2*g1*(r1-r0))


    final velocity with constant sea level gravity

    vg2=2016.24m/s=SQRT(2*g0*(r1-r0))


    average the two results = 1147.46m/s=(vg1+vg2)/2

    square average the results = 2035.41m/s=SQRT(vg1^2+vg2^2)
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Oct 21, 2013 #2

    gneill

    User Avatar

    Staff: Mentor

    Averaging results won't work here with acceleration varying with the inverse square of the distance.

    A better approach might be energy conservation.
     
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