Concept. Once it leaves the hand, a projectile only feels gravity.
Horizontal velocity stays constant; vertical velocity is pulled down by
g = 9.81 m/s². The path is a parabola.
Formulas (launch speed v₀, angle
θ):
vₓ = v₀cosθ v_y = v₀sinθ
Range R = v₀²·sin(2θ) / g
Max height H = (v₀sinθ)² / (2g)
Time of flight T = 2·v₀sinθ / g
Worked example. v₀ = 20 m/s, θ = 30°.
R = 20²·sin60° / 9.81 = 400·0.866 / 9.81 ≈ 35.3 m.
R = 20²·sin60° / 9.81 = 400·0.866 / 9.81 ≈ 35.3 m.
Famous Traps
45° myth. 45° gives max range only on flat
ground with no air resistance — not "always".
Complementary angles. θ and (90°−θ) give the
same range (e.g. 30° and 60°) — a classic "pick the other one".
vₓ is constant. Horizontal speed never changes in
flight. Only v_y does. Don't "slow down" vₓ.
Range: –
Max height: –
Flight time: –
vₓ: –
v_y: –
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