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Q.

A particle of mass m is projected from O with velocity v0cos⁡θi^+v0sin⁡θj^ At the same instant, another particle of mass 2m is projected from point P with v0k^ The velocity of 2nd  particle w.r.t first particle after time t=v0sin⁡θg is

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a

v0k^+gtj^+v0cos⁡θi^

b

v0k^−gtj^+v0cos⁡θi^

c

v0k^−v0cos⁡θi^

d

None of the above

answer is D.

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Detailed Solution

At t=v0sin⁡θq,v1→=v0cos⁡θi^ v2→=v0k^−gj^ ∴v2¯−v1¯=v0k^−gtj^−v0cos⁡θi^
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A particle of mass m is projected from O with velocity v0cos⁡θi^+v0sin⁡θj^ At the same instant, another particle of mass 2m is projected from point P with v0k^ The velocity of 2nd  particle w.r.t first particle after time t=v0sin⁡θg is