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Q.

Two bodies are thrown from the same point with the same velocity of projection angles of projection being complimentary angles. If $R_{1} and R_{2}$ are the ranges and $h_{1} and h_{2}$ are maximum heights respectively, then

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a

h_{1} + h_{2} = \frac{u^{2}}{2g}

b

none

c

both

d

R_{1} = R_{2} = \frac{u^{2}}{g} \sin 2 θ

answer is C.

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Detailed Solution

R_{1} = R_{2}

for complementary angle of projectile

$R_{1} = R_{2}$

$R_{1} = \frac{u^{2} \sin 2 θ}{g}, R_{2} = \frac{u^{2} \sin 2 θ}{g}$

$R_{1} = R_{2} = \frac{u^{2}}{g} \sin 2 θ$

$h_{1} + h_{2} = \frac{u^{2} \sin^{2} θ}{2g} + \frac{u^{2} \sin^{2} (90 - θ)}{g}$

$= \frac{u^{2}}{2g} (\sin^{2} θ + \cos^{2} θ)$

$h_{1} + h_{2} = \frac{u^{2}}{2g}$

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Two bodies are thrown from the same point with the same velocity of projection angles of projection being complimentary angles. If R1 and R2 are the ranges and h1 and h2 are maximum heights respectively, then