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=u2sin2θg=480m702sin2θ9.8=480⇒ sin2θ=480×9.870×70=2425⇒ cos2θ=725⇒2cos2θ−1=725⇒ cos2θ=1625⇒ cosθ=45⇒ θ=37∘So, angles of projection will be 37° and 53°. T1T2=2usin37∘g2usin53∘g=34H1H2=916umin1umin2=ucos37∘ucos53∘=43∵velocity at highest point =ucosθβ=θ+φ2=37+532=45