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Q.

A particle is projected with a velocity , so that its range on a horizontal plane is twice the greatest height attained. If g is acceleration due to gravity, then its range is

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a

4u25g

b

4g5v2

c

4u35g2

d

4u5g2

answer is A.

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Detailed Solution

H=u2sin2⁡θ2g  and  R=u2sin⁡2θg Since,R=2H, so u2sin⁡2θg=2u2sin2⁡θ2g or   2sin⁡θcos⁡θ=sin2⁡θ or tan⁡θ=2 ∴R=u22gsin⁡θcos⁡θ=2u2g2515=4u25g.
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A particle is projected with a velocity , so that its range on a horizontal plane is twice the greatest height attained. If g is acceleration due to gravity, then its range is