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Question

# A projectile has the same range R for two angles of projection. If T1 and T2 be the times of flight in the two cases, then R is

A
T1T2g
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B
T1T2g2
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C
(T21+T21)g
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D
T21+T222g
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Solution

## The correct option is B T1T2g2We know that for the two different angle of projection with the same range, the condition is the angles of projection should be complementary. Let (α) and (90−α) be angle of projection, measured from the horizontal. We know that ,time of flight is T=2usinθg, here θ is angle of projection. For the two different angle with same range T1=2usinαg,T2=2usin (90−α)g=2ucosαg Range of projectile: R=u2sin2αg=2u2sinαcosαg ⇒R=T1T2g2 Hence B is the correct option.

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