A shell is fired from a fixed artillery gun with an initial speed u such that it hits the target on the ground at a distance R from it. If t₁ and t₂ are the values of the time taken by it to hit the target in two possible ways, the product t₁t₂ is:
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Question

A shell is fired from a fixed artillery gun with an initial speed u such that it hits the target on the ground at a distance R from it. If t₁ and t₂ are the values of the time taken by it to hit the target in two possible ways, the product t₁t₂ is:

Options

G1 Physics · Accepted Answer

For the two possible projection angles giving the same range, the angles are complementary. Thus t₁ = 2u sinθ/g and t₂ = 2u cosθ/g. Their product is t₁t₂ = 4u²sinθcosθ/g² = 2u²sin2θ/g² = 2R/g. Hence option C.