Sports & Motion Analytics
Intermediate

Projectile Range

Horizontal distance a ball travels when launched at speed v and angle θ.

Formula

R=v2sin⁡(2θ)gR = \frac{v^2 \sin(2\theta)}{g}

Variables

RRange (m)
vLaunch speed (m/s)
θLaunch angle
gGravity 9.81 m/s²

Example

30 m/s at 45°: R = 900×1÷9.81 ≈ 91.7 m

Did You Know?

A 45° launch gives maximum range on flat ground — but for a shot put released above the ground the optimum is closer to 42°.

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