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Two particles are projected from the same point with same speed u at angles of projection α and β fromhorizontal. The maximum heights attained by them are h1 and h2 respectively, R is the range for both. Ift1 and t2 are their times of flight respectively, then which amongst the option{s) is/are incorrect?

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a

α+β=π2

b

R=4h1h2

c

tanα=t1t2=h1h2

d

tanα=h1h2

answer is D.

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Detailed Solution

Range becomes equal at complimentary angle. Hence,β=90°-α or α+β=90°=π/2(b) h1=u2sin2α2g ⇒ h2=u2cos2α2g As, β=90°-α ∴4h1h2=2u2sinαcosαg=u2sin2αg=R(c) t1t2=(2usinα/g)(2ucosα/g)=tanα(d) h1h2=tanα

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Two particles are projected from the same point with same speed u at angles of projection α and β fromhorizontal. The maximum heights attained by them are h1 and h2 respectively, R is the range for both. Ift1 and t2 are their times of flight respectively, then which amongst the option{s) is/are incorrect?