3.1.3—Projectile motion

For a projectile launched with speed u at angle θ, x=u cosθ·t and y=u sinθ·t−½gt² still describe the motion. A target at a different height changes the time and range equations, not the component model.

Write the target condition in x and y, eliminate t, and solve only for values consistent with t≥0. Do not use the level-ground range formula unless launch and landing heights are equal.

A ball launched from a platform can hit a lower target on the descending path; the second root of the height equation represents a later intersection, while a negative time is discarded.

The 45° maximum-range result is not universal: it assumes equal heights, uniform gravity and no air resistance.