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Question

Two particles A and B are projected simultaneously from a point situated on a horizontal plane. The particle A is projected vertically up with a velocity vA while the particle B is projected up at an angle of 30 with horizontal with a velocity vB. After 5 s, the particles were observed moving mutually perpendicular to each other. The velocity of projection of the particle vA and vB respectively are
(Take g=10 m/s2)

A
50 ms1,10 ms1
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B
100 ms1,50 ms1
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C
vA can have any value greater than 25 ms1, 100 ms1
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D
20 ms1,100 ms1
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Solution

The correct option is C vA can have any value greater than 25 ms1, 100 ms1
Velocity of A is always in the vertical direction. So, after 5 s velocity of B should be horizontal which happens when the projectile is at half the time of flight .
T2=5 or T=10 (where T is the time of flight)
T=2vBsinθg=10
or vB=100 m/s
Time of flight of A should be greater than 5 s
2vAsin90g>5
vA>25 m/s

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