I made a mistake! You can't integrate like that..
That makes it easier. Well, this is my first time using seperation ^^ so I might return..
Okay, my english is not perfect, but I hope you can understand what I'm talking about.
I'm having this subject about movement and air resistance. We're watching an object dropping in an area with air resistance. The resulting force on the object is (using Newton's 2. law):
F_res = -F_grav + F_air <=> ma = -mg + k*v^2
Let's introduce s(t) (don't know what it's called in english), and thereby s'(t) = v(t) and s''(t) = a(t).
After some paraphrasing, we get a(t) = k/m * v^2 - g <=> s''(t) = C * (s'(t))^2 - g with C = k/m
To find v(t) and s(t) we integrate, so
v(t) = 1/3 * C * t * (s(t))^3 - g * t + v_0 and
s(t) = 1/12 * C * t^2 * ((int.)s(t)dt)^4 - g * t^2 + v_0*t + s_0
Is this correct? How do I find s(t)??? My calculator can't find it.. Maybe I'm typing something wrong or I've done something wrong.. It's really urgent, please help!
s(t) is called the "displacement." It roughly corresponds to "position."
No, your work is not correct. You have a differential equation
You need to first write this as a velocity equation:
At the moment I can't remember how to solve this problem. Perhaps one of the other Helpers will post on this.
Yes, I've concluded that as well - but thanks And thank you for the information.
But now I'm stuck again. I've spent 2-3 hours working with this and I've recieved a lot of help, but I haven't been tought how to deal with separation in differential calculations - so I beg you, please, somebody, show me how to solve the following step-by-step and explain to me, how you do. Please, it's very important!
where A is the integration constant, set by the initial conditions.
As you can see this is not a nice equation to solve for v, but it can be done:
I'll leave it to you to integrate this to get s(t). (This is even less pretty, but still doable.)
Topsquark, thank you thank you thank you!!
So A must be my .
There just 2 steps I don't get, though..
How do you isolate ? And how do you go from (4) to (5) ?
If noone has the time to help me out, I'll return in the morning - in Denmark it's 3 AM
See this thread for further help: