Two balls are projected with the same initial speed at different angles. The maximum height of the first is 8 times that of the second. If their times of flight are T₁ and T₂, then T₁:T₂ is:
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Question

Two balls are projected with the same initial speed at different angles. The maximum height of the first is 8 times that of the second. If their times of flight are T₁ and T₂, then T₁:T₂ is:

G1 Physics · Accepted Answer

For the same projection speed u, maximum height is H = u²sin²θ/(2g). Given H₁ = 8H₂: sin²θ₁ = 8sin²θ₂. Therefore, sinθ₁/sinθ₂ = √8 = 2√2. Time of flight is T = 2u sinθ/g. Thus, T₁/T₂ = sinθ₁/sinθ₂ = 2√2. Hence, T₁:T₂ = 2√2:1. Correct option: A.