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Question

Two particles A and B are shot from the same height at t=0 in opposite directions with horizontal velocities 3m/s and 4m/s respectively. If they are subjected to the same vertical acceleration due to gravity (g=9.8m/s2). the distance between them when their velocity vectors become mutually perpendicular is:

A
1.059m
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B
1.412m
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C
2.474m
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D
9.8m
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Solution

The correct option is C 2.474m
Let the velocity of A be 3^i+u^j=VA
Let the velocity of B be 4^i+u^j=VB
where 'u' is the vertical velocity which will be same for both as both are thrown simultaneously. Now,
VA.VB=0(3^i+u^j)(4^i+v^j)=012+u2=0u=12u=0+9.8tt=129.8s
Relative velocity of A w.r.t B =3(4)=3+4=7m/s
Distance =7×129.8=2.474m

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