Projectile Motion analytical solutions

[Sir_Matt]

Hi, I'm trying to find the analytical solutions to projectile motion, and not just the approximations.I know the Euler approximation for velocity is the inital velocity - acceleration*time, but what is the more accurate analytical solution for velocity.Thank you.

 

[Cyosis]

That depends on the environment the projectile travels through. The equation you have is perfectly analytical and exact for a projectile that travels only in a constant gravitational field (within the regime of classical mechanics).

To find a solution for a certain environment you will need to start with $F= dp/dt$. On the left side you have the vector sum of all forces acting upon the projectile. Then all you have to do is solve the differential equation. Unfortunately that is not always possible analytically at which point we'll have to do it numerically.

 

[Sir_Matt]

Yes no drag, changing air densities or anything.
Ok so this is the most accurate equation. I will use it then.
Thanks.