3.1.1—Projectile motion

Ignoring air resistance, horizontal acceleration is zero and vertical acceleration is −g. With initial speed u at angle θ, x=u cosθ·t and y=u sinθ·t−½gt².

Treat the two components independently, then eliminate t or use symmetry. The launch and landing heights must be stated before using range or time-of-flight formulas.

For level ground, time of flight is 2u sinθ/g and range is u²sin2θ/g. The maximum range occurs at 45° only under this level-ground, no-drag model.

The velocity is not constant as a vector; only its horizontal component is constant, and gravity acts throughout the flight.