A particle of mass $$1$$ kg is thrown vertically upward with speed $$100$$ $$ms-1$$ . After $$5$$ s, it explodes into twoparts. One part of mass $$400$$ g emerges with speed $$25$$ $$ms-1in$$ downward direction, what is the velocity of other part just after explosion? (Take$$, g $$=$$ $$10$$ $$ms-2)

Question

A particle of mass $$1$$ kg is thrown vertically upward with speed $$100$$ $$ms-1$$ . After $$5$$ s, it explodes into twoparts. One part of mass $$400$$ g emerges with speed $$25$$ $$ms-1in$$ downward direction, what is the velocity of other part just after explosion? (Take$$, g $$=$$ $$10$$ $$ms-2)

Infinity Learn · Accepted Answer

Velocity of particle after $$5$$ s,               $$v=u=gt=100-10$$×$$5$$                  $$=100-50=50$$ $$ms-1$$                           (upwards)Conservation$$ of linear momentum gives               Mv $$=$$ $$m1v1+m2v2$$                                             …$$(i)Taking$$ upward direction positive,                   $$v1=-25ms-1$$, $$v=50$$ $$ms-1$$                   M $$=$$ $$1kg$$, $$m1=400$$ g $$=$$ $$0.4$$ kg                   $$m2$$ $$=$$ $$M-m1=1-0.4=0.6$$ kgFrom Eq. $$(i), we get           $$1$$×$$50=0.4$$×$$(-25)+0.6v2$$  or $$v2$$ $$=$$ $$100$$ $$ms-1$$  (upwards)

A particle of mass 1 kg is thrown vertically upward with speed 100 ms-1 . After 5 s, it explodes into twoparts. One part of mass 400 g emerges with speed 25 ms-1in downward direction, what is the velocity of other part just after explosion? (Take, g = 10 ms-2)

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