Derivation of the Range of a Projectile
| Vx = Xx / t | Vx = V in x direction; t = time in air |
| Xx = Range = (Vx)(t) | Vx = (Vocosq ) |
| Xx = (Vocosq )(t) t = (2Vy)/g; | Vy = V in y direction |
| Xx = (Vocosq ) ([2Vy]/g) | Vy = (Vosinq ); substitute |
| Xx = (Vocosq ) * ([-2(Vysinq ]/g) | 2sinq * cosq = sin2q |
| Xx = (-Vo2 sin2q ) / g |
Xx = (-Vo2 sin2q ) / g
Note: to find out how to derive the time in the air of a projectile see the derivation -
Time in the Air of a Projectile.
| Vx = Xx / t | Vx = V in x direction; t = time in air |
| Xx = Range = (Vx)(t) | Vx = V |
| Xx = V * (sqr. root(2H/g) | t = sqr. Root(2H/g) |
Xx = V * (sqr. root(2H/g)
Note: to find out how to derive the time in the air of a projectile see the derivation -