# Parabolic Shot

From Synfig Studio :: Documentation

This is an small tutorial to show how make an object to follow a path given by a mathematical function as a reply for a requested tutorial.

## Mathematical function to follow

We're going to simulate a cannon shot. A cannon bullet describes a parabolic trajectory after it is shot by the cannon. The mathematical equations that govern the trajectory are:

X=V0x*t+X0 Y=-0.5*G*t²+V0y*t+Y0

where:

t = the current time for the mathematical equation X = the 'x' coordinate of the bullet at a time 't' Y = the 'y' coordinate of the bullet at a time 't' X0 = the 'x' position of the bullet at time t = 0 Y0 = the 'y' position of the bullet at time t = 0 V0x = the 'x' component of the velocity when shot (t = 0) V0y = the 'y' component of the velocity when shot (t = 0) G = the gravity's acceleration.

You usually have the angle and the velocity modulus instead of its components. The decomposition is quite easy:

V0x = V0*cos(phi) V0y = V0*sin(phi)

where:

V0 = the velocity when shot (t = 0) phi = the shooting angle.