On 05/31/2012 06:24 AM, Jaime Villate wrote:
> Hi,
> you might have seen a picture of the Indian teenager holding a poster
> with the equation he recently
> discovered. If you are curious to know what it is about, here is a
> possible derivation of the equation.
>
> The motion of a projectile on a vertical plane xy is due to two external
> forces, its weight [0, -m*g],
> and the air resistance (Fr) which is proportional to the square of the
> speed v (v=sqrt(vx^2+vy^2) and
> it is always opposite to the velocity [vx,vy]
This is fine as a toy math problem, but the proportionality in real
physical problems is not a constant. In fact it's a function of the
Reynold's number (and the shape). I used the spherical projectile
problem with air drag in a class on programming in matlab where students
solved it using numerical methods to find things like the range of a
particular projectile, and answer questions like whether the mythbusters
could put their cannon ball through your window given some initial
conditions (a reference to an unfortunate accident that the producers of
that TV show had, where thankfully by some miracle no one was hurt).
The formula I used was taken from this paper (link below), and the
problem is a fairly flexible one that can be adapted to many different
instructional purposes from programming, to fluid mechanics, to
numerical solutions of differential equations, optimization, statistical
analysis, and all sorts of good stuff
http://www.chem.mtu.edu/~fmorriso/DataCorrelationForSphereDrag2010.pdf