How it’s calculated
Without air resistance, a projectile moves horizontally at constant speed while gravity accelerates it downward. Treating the two directions separately gives these results (launch height h₀ above the landing point):
Example (OpenStax University Physics Vol. 1 §4.3, fireworks shell): v₀ = 70.0 m/s at 75.0° with g = 9.8 m/s² gives v_y = 67.6 m/s, a peak height of 67.6² ÷ (2 × 9.8) = 233 m after 6.90 s, 125 m downrange.
Real projectiles fall short of these figures because of air drag, especially light or fast objects.
Frequently asked questions
What angle gives the maximum range?
45° on level ground, ignoring air resistance. Launching from a height, the best angle is a little below 45°.
Why do 30° and 60° give the same range?
On level ground the range depends on sin 2θ, and sin 60° = sin 120°. Complementary angles land in the same place, but the steeper one flies higher and longer.
Does mass matter?
Not without air resistance: all objects fall with the same acceleration g.
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Sources
- University Physics Volume 1, §4.3 Projectile Motion — OpenStax
- CODATA value: standard acceleration of gravity — NIST
Formulas are taken from the free public references above. Results are provided “as is” for informational and educational purposes only. See our disclaimer.
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