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Two particles are projected from the same point with same speed u at angles of projection α and β from
horizontal. The maximum heights attained by them are h1 and h2 respectively, R is the range for both. If
t1 and t2 are their times of flight respectively, then which amongst the option{s) is/are incorrect?

a
α+β=π2
b
R=4h1h2
c
tanα=t1t2=h1h2
d
tanα=h1h2

detailed solution

Correct option is D

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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