2.1.9—Motion due to a uniform velocity in one direction and a uniform acceleration

For a projectile, horizontal velocity remains constant while vertical acceleration is −g. Position is described by x=u_xt and y=u_yt−½gt².

Solve components with the same time variable, then eliminate time only after applying launch and landing conditions. Air resistance is excluded by the ideal model.

A horizontal launch from height h has flight time √(2h/g) and horizontal range u√(2h/g).

The horizontal and vertical motions share time but not acceleration; gravity does not create horizontal acceleration.