1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Object falling towards moon

  1. Mar 13, 2010 #1
    1. The problem statement, all variables and given/known data
    An object is dropped from a distanse of 2*R(moon radius) from moon senter.
    How many seconds does it take until impact with moon, and in what speed will it hit?

    The distanse of the fall will be 1.74*10^6 m. The problem is the not so constant accleration.. ;)

    gravity constant: G := 6.67*10^(-11)
    moon mass M := 0.0735^24 kg
    moon radius R := 1.74*10^6 m



    2. Relevant equations

    gravity(accleration) is
    g=G*M/R^2

    So a(x)=(G*M)/(2*R - x)^2 , x = meter fallen x{0..R)


    3. The attempt at a solution
    I've calculated the speed at impact:

    Average accleration:
    > A:=(G*M)/(2*R - x)^2
    > Aa := (int(A, x = 0 .. R))/R;
    0.8096264368

    Time using x= 0.5*a*t^2
    > T := solve(R = 0.5*Aa*t^2, t);
    -2073.229031, 2073.229031

    This time is found using constant accleration, so it isnt the correct one...
    but it will work for finding the speed of impact.

    Speed
    > V := T*Aa;
    -1678.541033, 1678.541033
    So it will hit at 1678,54 m/s

    but for how long will it fall?
     
  2. jcsd
  3. Mar 13, 2010 #2
    You have acceleration as a function of distance. Put it in the expression a = v*dv/dx.That way you can obtain velocity as a function of distance by integrating. That will solve the first part of your problem. For time you can write v as dx/dt. Now if you put that and integrate you have distance as a function of time.
     
  4. Mar 13, 2010 #3
    Thanks aim!

    I got the correct velocity using your method, but i dont figure out the distanse as a function of time...

    Could you please try to explain it again, a bit more detailed? :)
     
  5. Mar 13, 2010 #4
    Ok you figured out velocity as a function of distance(x). Now what you do is write v as dx/dt. You will notice that the equation now contains x and t only. A little rearrangement and integration and you can express x as function of t.
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook