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Question

A projectile can have the same range R for two angles of projection. If t1 and t2 be the time of flight in the two cases then prove that t1t2=2R/g

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Solution

For a projectile having same range for two angle of projection , both angles should be complementary to each other, i.e, if one angle is α, then other will be β=900α
so, t1=2usinαg and t2=2usinβg=2usin(900α)g=2ucosαg

so, t1t2=4u2sinαcosαg2=2Rg

since, R=(u2sin2θ)/g=2usinθcosθg

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