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MotionLab
Launch speed and angle in — range, max height, and flight time out.
Projectile motion is solved by treating horizontal and vertical motion completely separately — horizontal velocity stays constant (ignoring air resistance) while vertical velocity is governed entirely by gravity, and combining the two gives the full trajectory.
For a given launch speed on flat ground, a 45° launch angle produces the maximum horizontal range — any steeper wastes energy going too high, any shallower doesn't stay airborne long enough, which is why this angle shows up constantly in sports and ballistics.
Range (m)
40.775
R = v₀²·sin(2θ) / g
What you entered
Horizontal velocity: vₓ = v₀·cos(θ)
20 × cos(45°)= 14.1421Vertical velocity: vy = v₀·sin(θ)
20 × sin(45°)= 14.1421Time of flight: t = 2vy ÷ g
2 × 14.1421 ÷ 9.81= 2.8832 sMax height: h = vy² ÷ 2g
14.1421² ÷ (2 × 9.81)= 10.1937 mRange: R = v₀²·sin(2θ) ÷ g
20² × sin(90°) ÷ 9.81= 40.7747 mResult
Range (m): 40.775
Launched at 20 m/s and 45°, the projectile travels 40.77m, reaching a max height of 10.19m over 2.88s.