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Question

Two particles projected from the same point with same speed u at angles of projection α and β strike the horizontal ground at the same point. If h1 and h2 are the maximum heights attained by projectiles, R be the range for both and t1 and t2 be their time of flights respectively, then

A
α+β=π2
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B
R=4h1h2
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C
t1t2=tanα
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D
tanα=h1h2
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Solution

The correct options are
A α+β=π2
B t1t2=tanα
C R=4h1h2
D tanα=h1h2
A B
θ=αθ=β
R=RR=R
H=h1H=h2
u=uu=u
t1=2usinαgt2=2usinβg
t1t2=2usinαgg2usinβ=sinαsin(π/2α)=tanα (Option C)
R1=u2sin2αgR2=u2sin2βg
R1=R2sin2α=sin2β
2α=π2β
α+β=π/2 (Option A)
H1=u2sin2α2g H2=u2sin2β2g
H1H2=(u2sin2α2g2gu2sin2β)1/2
H1H2=sinαsinβ=sinαsin(π/2α)=tanα (Option D)
H1H2=u2sinαsinβ2g=2u24gsinαsin(π/2α)
H1H2=u24gsin2α
4H1H2=R (Option B)

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