Hello, this is my first post, been lurking here for awhile.(adsbygoogle = window.adsbygoogle || []).push({});

I made up this physics problem which involves a particle in 2-D. The particle has an initial velocity (Vo) or initial kinetic energy (KEo) launched at some angle. Once the particle is fired the only forces acting on it are air friction, which is in the opposite direction to its velocity and the particles own weight.

Here's how I modeled the air friction:

The particles kinetic energy (KE) decreases according this function of time.

KE(t) = KEo e^(-c*t), where c is some constant (with inverse seconds for units, just to keep the units consitant), a percentage, between 1 and 0. I used the particles KE as behaving like a charged capacitor discharging through a resistor, that's how I thought of the decreasing exponential function. I don't know if this is an accurate way to model air friction, just doing this for fun.

Find: a function of the particles X-Y position according to time.

Do I sound crazy?

This is what I've done so far.

I found the particles speed as a function of time:

v(t) = sqrt(Vo^2*e^(c*t)), this is a magnitude

I then looked as the forces:

The weight: W = m*g, in the negative y direction, duh

I'm unable to find the air friction force. If I knew the magnitude of the air friction force with respect to time I'd be fine.

I then used F = dp/dt (differential of linear momentum with respect to time) on the particles velocity to be used to find how the direction of the particle is changed by the forces. I don't know if you can do this?

I found the particles linear momentum, m*v(t); than differentiated with respect to time to express it as a force. Can you do that, to find out how the direction of the particle is changed?

Alright enough babbling, anyone have any clue what I'm talking about?

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# Some weird particle problem I invented. Long read.

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