- #1
nathanthegreat
- 15
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Homework Statement
So, I'm building a "Monkey Gun" and I want to be able to find the instantaneous velocity of my dart at a certain time. I shoot the gun at some angle, θ. The problem is, if I divide the velocity into x and y components, each depends on and impacts the other (the force from the direction will change the x velocity, changing the total velocity, changing the y velocity, etc.). I did a quick calculation assuming the dart remained at 60 m/s and I found a change in velocity of about 25 m/s, which is quite substantial. I know it won't actually be this much because the dart doesn't remain at 60 m/s, but it will still impact the dart.
I know I can mainly just ignore air resistance because the target is a decent size, but this is something I want to know for future experiments.
Homework Equations
$$F=ma$$ $$F_d =.5 \rho C_D A v^2$$
The Attempt at a Solution
I derived an equation for the instantaneous velocity for a freely falling object and got $$v(t)=√((mg-(mg-kv_0^2)e^((-2k)/m(∆t)))/k)$$. Now how can I find something like this in two dimensions? I know the y component will need to divided into a function for when the projectile is going up and a different one when it is coming down.
-Nathan