Two projectiles are fired from ground with same initial speeds from same point at angles ( 4 5 ∘ + α ) and ( 4 5 ∘ − α ) with horizontal direction. The ratio of their times of flights is

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θ 1 ​ = 45 + α ; θ 2 ​ = 45 − α Time of flight, T = g 2 v s i n θ ​ T 2 ​ T 1 ​ ​ = s i n ( 45 − α ) s i n ( 45 + α ) ​ T 2 ​ T 1 ​ ​ = 2 ​ 1 ​ c o s α − 2 ​ 1 ​ s i n α 2 ​ 1 ​ c o s α + 2 ​ 1 ​ s i n α ​ T 2 ​ T 1 ​ ​ = c o s α − s i n α c o s α + s i n α ​ = 1 − t a n α 1 + t a n α ​

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