Problem is, the tan() equation is wrong. It does not produce realistic results. With an initial speed of 20m/s, and t = 2 the equation produces a velocity of 19.84m/s. Which is not possible. The actual velocity should be closer to 5.7m/s as predicted by the previous solution. There is a problem...
V = \frac {V_0}{1 + \mu V_0 t}
is the solution to the previous problem [Thanks Tide!] and I want a to know how to do it. I can't get figure out how to get this solution by separating and integrating. When I do that, I get:
V = \frac {tan( t \sqrt \mu \sqrt \beta) * \sqrt \mu} {\sqrt...
Alright. I've had quite the difficulty figuring out how you got from my difference equation to the solution. I've hunted through my math books and through numerous sources on the internet. I really want to know how to do this, so a couple of intermediate steps would be nice to see. I've found my...
Oops. Sorry, the t should have been dt. Corrected:
dV = - \mu V^2 dt - \beta dt
dH = \gamma V^2 dt - \alpha dt
So, how do I integrate these? Let's take the first one and divide by dt. Then I get:
\frac {dV} {dt} = - \mu V^2 - \beta
Now what...
I know at some point, years ago, I could differential equations in my sleep. But now after going through my old math book and reading a number of the threads here, I'm really confused. The problem I am looking to solve looks like this:
dV = - \mu V^2 t - \beta t
where mu and beta are...
I need some help. Our company is holding a paper airplane constest for distance and I've been trying to work out the math to find the best mass, wing-span, wing-chord, launch angle, etc. combination. I've worked through a bunch of the math but I've just been stumped by what appears to be a...