How to calculate projectile motion with unit directional vector

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

Solution

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

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 ...

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]