Two projectiles are fired from the same point with the same speed at angles (45°+α) and (45°-α) above the horizontal. The ratio of their times of flight T₁/T₂ is:
Options

Question

Two projectiles are fired from the same point with the same speed at angles (45°+α) and (45°-α) above the horizontal. The ratio of their times of flight T₁/T₂ is:

G1 Physics · Accepted Answer

Time of flight for a projectile launched from ground is T = 2u sinθ/g. Therefore, T₁/T₂ = sin(45°+α)/sin(45°-α). Using sin(45°±α) = (1/√2)(cosα ± sinα), we get T₁/T₂ = (cosα+sinα)/(cosα-sinα). Divide numerator and denominator by cosα: T₁/T₂ = (1+tanα)/(1-tanα). Correct option: D.