Projectile motion is the superposition of two independent motions:

Horizontal (x-direction):

• a_x = 0 (no air resistance)
• v_x = u*cos(theta) = constant throughout flight
• x = u*cos(theta) * t

Vertical (y-direction):

• a_y = -g (upward positive)
• v_y = usin(theta) - gt
• y = u*sin(theta)t - (1/2)gt^2

Independence principle: Horizontal and vertical motions do not affect each other. A bullet fired horizontally and one dropped from the same height hit the ground at the SAME time.

Equation of trajectory (eliminate t): y = xtan(theta) - gx^2 / (2u^2cos^2(theta))

This is a parabola (y = ax - bx^2 form).