1. Not finding help here? Sign up for a free 30min 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!

Fall of Object

  1. Jan 25, 2006 #1
    If it takes an object at distance x from the surface of the Earth 17.5 hours to fall from space onto the surface of the Earth, how can we calculate x? The object initially has zero speed.

    I find this question hard because I've only done problems involving acceleration as a function of time, and not as a function of distance. :redface: Can anyone show me how to derive an equation of acceleration as a function of time?
     
  2. jcsd
  3. Jan 25, 2006 #2

    siddharth

    User Avatar
    Homework Helper
    Gold Member

    You can use [tex] \frac{dv}{dt} = (\frac{dv}{dr})(\frac{dr}{dt}) = v \frac{dv}{dr} [/tex]
    So I think from this you can first find v(r) and then r(t) and use that to find x.
     
  4. Jan 25, 2006 #3
    The first thing you may want to realize is that acceleration is a function of distance between the object and the center of the earth, and that the distance is a function of time.
     
  5. Jan 25, 2006 #4
    I know [tex]\frac{dv}{dt} = \frac{GM}{r^2}[/tex] but I can't figure out how this may be used to obtain v as a function of r.
    How is it possible to solve the equation [tex]\frac{d^{2}r}{dt^2}=\frac{GM}{(R+r)^2}[/tex], where R is the radius of the Earth? I have not had much calculus yet, so I have not touched on solving differential equations of this difficulty.
     
    Last edited: Jan 25, 2006
  6. Jan 25, 2006 #5

    siddharth

    User Avatar
    Homework Helper
    Gold Member

    You have

    [tex]\frac{dv}{dt} = \frac{GM}{r^2}[/tex]

    Now, as I said in my previous post,

    [tex] \frac{dv}{dt} = (\frac{dv}{dr})(\frac{dr}{dt}) = v \frac{dv}{dr} [/tex]

    So,
    [tex]v\frac{dv}{dr} = \frac{GM}{r^2}[/tex]

    Now, can you find v(r) from this diff equation?
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Fall of Object
  1. Falling Object (Replies: 20)

  2. Falling object (Replies: 4)

  3. Falling Object (Replies: 3)

  4. Falling Object (Replies: 6)

  5. Falling Objects (Replies: 2)

Loading...