Question

A firecracker travels straight up at 75.0 m/s and explodes into two pieces. The smaller piece carries one third of the firecracker’s mass and shoots off horizontally at 48.0 m/s west. Determine the speed and direction of the other piece directly after the explosion.
momentum is conserved , vertically and horizontally

the larger piece carries all of the vertical momentum , and horizontal momentum equal and opposite to the smaller piece

find the vertical and horizontal momentum vectors and add them
bobpursley
we will be happy to critique your work.

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