At Which Angle the Stone Is Projected for Maximum Horizontal Range?
At which angle the stone is projected for maximum horizontal range — this is a central question in projectile motion, and physics shows that when all ideal conditions are met, the optimum projection angle is 45°.
The Maths: Projectile Range Formula
For a projectile launched from level ground (same initial and final height), with initial speed v₀ and launch angle θ, the horizontal range R is given by:
R = (v₀² / g) · sin (2θ) :contentReference[oaicite:0]{index=0}
Why 45° Gives Maximum Range
The sine function sin(2θ) reaches its maximum value (1) when 2θ = 90°, i.e. θ = 45°. So at θ = 45°, range R becomes maximum (Rₘₐₓ = v₀² / g) under ideal conditions (no air resistance, equal launch and landing heights). :contentReference[oaicite:1]{index=1}
Implications and Important Conditions
- The launch and landing levels must be the same (ground to ground). :contentReference[oaicite:2]{index=2}
- No air resistance or external forces — otherwise optimal angle may change. :contentReference[oaicite:3]{index=3}
- For different conditions (height difference, drag, wind), the “45° rule” might not hold strictly. :contentReference[oaicite:4]{index=4}
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