How to calculate projectile motion with unit directional vector

Question

i have already found the math for dealing with projectile motion but the different with mine was the directional vector and time provided.

In my code , my directional vector was -1 to 1 and time was an interval time.

How do I use those vector and time to calculate the new directional vector due to gravity?

Please help

Answer 1

I assume 3D space (with gravity directing in -Y direction)

1. init

   // player / gun parameters
   const float v0 = ???;             // [m/s] gun projectile escape velocity
   float direction[3] = { ?,?,? };  // [-] your unit direction vector
   float position[3] =  { ?,?,? };  // [m] your player position + gun barrel offset
   
   // projectile parameters
   float a[3]={0,-9.81,0};   // [m/s^2] actual acceleration (just gravity in down direction)
   float v[3]=direction*v0;  // [m/s] actual velocity
   float p[3]=position;      // [m] actual position
   

   if you want to be precise add to v also your players velocity vector. If your projectile is rocket then add to a also its trust acceleration in its direction ...

2. update in some timer

   const float dt = 0.001; // [s] update 'timer' period
   
   v += a*dt;
   p += v*dt;
   

   here you can add tests like: hit something, hit ground, ... also friction is a good idea ...

   F=c0*|v|^2; for air
   F=c1*|v|^3; for liquid
   

   in direction (-v/|v|) so add to start of update this:

   a={0,-9.81,0}
   a-=v*c0*|v|/m; // or a-=v*c1*|v|^2/m;
   

   where c0,c1 are friction constants (try ~0.01) and m is the projectile mass [kg]