A particle flies away from the surface of the fluid at time t = t1. The surface model gives us the initial velocity vector of the particle v1 = v(t1) and its initial position vector r1 = r(t1). We want to describe the motion of the particle in 3D-space after it has left the surface. Ignoring air resistance, its acceleration is given by
a(t) = -gkwhere g ≈ 9.8 m/s² is the acceleration due to gravity and k is the standard basis vector <0,0,1>.
v(t) = -gtk+cwhere c is a constant vector.
r(t) = -½gt²k+ct+dwhere d is a constant vector.