P02-050 – Property of the Path of the Projectile

Property of the path of the projectile:

For a given initial velocity $\overrightarrow{v_0}$ launch angles of ${\theta }_0$ and $90-{\theta }_0$ achieve the same range.

If ${\theta }_0<45{}^\circ $

The projectile then has more horizontal velocity than vertical velocity: it spends little time being airborne but since it travels fast horizontally, it covers the distance $x_M$.

If ${\theta }_0>45{}^\circ $

The projectile then has more vertical velocity than horizontal velocity: it spends more time being airborne which compensates for its low horizontal speed and still allows it to cover the distance $x_M$.