simulating arrow

If you put t (time) on the x (horizontal) axis, and x on the y (vertical) axis then you get a "two-dimensional equation" (Or at least a two-dimensional plot).

The equation is exactly the same for all dimensions:

p(t) = p(0) + v(0) t + a t²/2

Or, expanded for x, y and z:

p_x(t) = p_x(0) + v_x(0) t + a_x t²/2
p_y(t) = p_y(0) + v_y(0) t + a_y t²/2
p_z(t) = p_z(0) + v_z(0) t + a_z t²/2

However, if the only acceleration is gravity, pointing straight down, then a_x and a_y wil be zero, resulting in:

p_x(t) = p_x(0) + v_x(0) t
p_y(t) = p_y(0) + v_y(0) t
p_z(t) = p_z(0) + v_z(0) t + a_z t²/2

Actually that is already a multi-dimensional equation, you just have to look at x0,v0 and a0 as vectors.

One more thing, that is not really a projectile equation, it is just an equation for particle movement with initial velocity and fixed acceleration.

if you replace a0 with -g (-9.81m/s2 on the vertical axis) you'll get your projectile equation.

EDIT: late

I see I mixed it up.

tinu, check out Trajectory of a projectile on Wikipedia. It contains everything you need.