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Q.

Two particles A and B projected along different directions from the same point P on the ground with the same velocity of 70 m/s in the same vertical plane. They hit the ground at the same point Q such that PQ = 480 m, then (take, g = 9.8 m/s2)

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a

ratio of their times of flight is 4 : 5

b

ratio of their maximum heights is 9 : 16

c

ratio of their minimum speeds during flights is 4 : 3

d

the bisector of the angle between their directions of projection makes 45o with horizontal

answer is B.

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Detailed Solution

R=u2sin⁡2θg=480m702sin⁡2θ9.8=480⇒ sin⁡2θ=480×9.870×70=2425⇒ cos⁡2θ=725⇒2cos2⁡θ−1=725⇒ cos2⁡θ=1625⇒ cos⁡θ=45⇒ θ=37∘So, angles of projection will be 37° and 53°. T1T2=2usin⁡37∘g2usin⁡53∘g=34H1H2=916umin1umin2=ucos⁡37∘ucos⁡53∘=43∵velocity at highest point =ucosθβ=θ+φ2=37+532=45
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