(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Restate the vertical projectile problem in a properly scaled form. (suppose x<<R).

d2x/dt^2=-g(R^2)/(x+R)^2

Initial conditions: x(0)=0, dx(0)/dt=Vo

Find the approximate solution accurate up to order O(1) and O(e), where r is a small dimensionless parameter. (i.e. the solution is given by a function f(e)).

Hint: Suppose 1/(1-e) is a term involving the small parameter e (i.e. e<<1) in the dimensionless equation, do the taylor expansion 1/(1-e)=1+e+....If we approximate 1(1-e) by 1 in the equation then we will obtain the O(1) solution, if we approximate 1/(1-e) by 1+e in the equation, we will obtain the O(e) solution.

2. Relevant equations

3. The attempt at a solution

I properly nondimensionalized the equation, getting the following:

d2y/dT^2=-K/(y+1)^2 where K = gR/Vo^2.

Now, as for the O(1) and O(e) stuff, I am completely baffled as to what the problem is asking for. Can someone please explain to me what exactly I am supposed to be doing?

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# Homework Help: Scaling of the vertical projectile problem nondimensionalization

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