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A bomb explodes and 3 pieces are flying in different directions.

Piece 1 : weighs 2kg and is travelling at the North East direction

Piece 2 : weighs 1kg and is travelling in the south direction ( exactly downards )

Piece 3 : weighs 3 kg and is travelling in the west direction ( exactly to the left )

Find the velocity and direction that Piece 1 is travelling at.

I know to use the momentum equation twice , one with the horizontal direction and one on the vertical direction.

Horizontal:

M1V1(initial)+M2V2(initial)+M3V3(initial) = M1V1(Final)+M2V2(Final)+M3V3(final)

Since all the initial velocities are 0 ( because bomb was at rest before explosion , the entire left side is equal to zero)

0 = 2kg ( V1F ) cosx + 1kg ( 30 m/s) cos 90 + 3kg ( 20 m/s ) Cos 180

= 2kg (V1F) cosx - 60 Kg/m/s

30 m/s = V1F cosx

Above , i canceled M2V2(FINAL) because i set that as the reference direction and angle , so it counts as 0. and i did minus 60 kg/m/s because its to the negative direction.

Vertical :

M1V1(initial)+M2V2(initial)+M3V3(initial) = M1V1(Final)+M2V2(Final)+M3V3(final)

Since all the initial velocities are 0 ( because bomb was at rest before explosion , the entire left side is equal to zero)

0 = 2kg ( V1F ) sinx + 1kg ( 30 m/s) sin 90 + 3kg ( 20 m/s ) sin 180

= 2kg ( V1F) sinx - 30 Kg/m/s

15 m/s = V1F sinx

Then divided the final equations to get

Sinx V1F 15 m/s

--------- = -------

Cosx V1F 30 m/s

Tanx V1F = .5 m/s

now i have no idea wat to do to find the direction and speed :( can anyone help please?