About the trajectory of an idealized projectile

Given that the air resistance is negligible, the trajectory of a projectile is a combination of horizontal motion with constant velocity and vertical motion with constant acceleration.

For the trajectory part, what does v0 mean?  If v0 is a vector, it should have x and y elements. Should we use the magnitude of the vector, or the value of x or y for calculations?

Do x(t) and y(t) refer to displacement?

Recall from high school: rectilinear motion with uniform acceleration a v = vo + at 1 x xo = vot +at? v? = v3 + 2a(x xo) 1 Trajectory: x(t) = v, cos a, t, y(t) = vo sin a, t - g Eliminate t = y = (tan ao)x 2v3 cos? ao i.e. y = bx cx? a parabola motion with A typical projectile: at the top, 0 = vy = vo sin ao - gT =T = vo sin ao /g y uniform downward acceleration g, max. height = vo sin ao T U3x a Ja U 1x V3y a, = vi sin? ao Uoy 2g ao O vOx x motion, no acceleration, range = vo cos a, (2T) = 2v3 sin a, cos ao /g