NILS B=D6RJESSON wrote:
A body move in Earth's gravity g=3D10.
The resistance is proportionell to the square of the velecito.
The resistance due to friction with air.
With units choisen to make the equation's look good:
v_x'=3D-00-v_x.|v|
v_y'=3D-10-v_y.|v|
x0=3D0 y0=3D0 v_x0 and v_y0 given.
v_x is velecito along the ground.
v_y is velecito up.
00 is gravity along the ground
-10 is gravity up.
|v| is the magnitude of the velecito.
I have made Numerical calculation in Excel and if
The beginning velecito is BIG >10^100.:
The orbit looks like:
/|
/ |
/ |
/ |
/ |
/_____|
ground
The amount of resistance depends on the shape of
the projectile, and that would affect the trajectory.
This isn't a very good model of an artillery shell (heavy,
streamlined, resistive force small compared to mass) in
air. It's probably not a bad model of the same artillery
shell fired underwater.
It confirms the medial theorys about projetile.
But does it confirm actual observation?
The resistance can have been BIGGER back in time.
And/or the earth gravity was lighter.
I think you're saying there was a medieval theory of
projectiles that predicted this shape for trajectories,
prior to the invention of cannons.
No, the laws of physics haven't changed. Our ability
to fire projectiles has improved. But I don't think that
even rocks thrown by catapult would follow this highly
resistive model.
- Randy
.
