A projectile is fired at 45°. If R is its horizontal range and S is its actual path length, then:
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A projectile is fired at 45°. If R is its horizontal range and S is its actual path length, then:

G1 Physics · Accepted Answer

At θ=45°, R = u²/g. Using the trajectory-length result, S = (u²/g) [sin45° + cos²45° ln(sec45°+tan45°)]. Now sin45°=1/√2, cos²45°=1/2, sec45°+tan45° = √2+1. Therefore S/R = 1/√2 + (1/2)ln(1+√2).