Afirecracker in a coconut blows the coconut into three pieces. two pieces of equal mass fly off south and west, perpendicular to each other, at speed v0. the third piece has twice the mass as the other two. what are the speed and direction of the third piece? give the direction as an angle east of north.

As per momentum conservation theory

If net force on a system is zero then initial momentum of the system will be equal to final momentum of that system.

Since initially coconut is at rest so initial momentum is zero

Here it break into three pieces such that two parts of same mass while third part is of double mass

now we can say

here we know that two parts fly off with same speed v0 along south and west directions

now we will have

so here magnitude of the speed of the third part will be

and the direction of the third part will be along North East direction

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