Grade 12 Physics Bomb explosion

[Shin-]

Question:
A bomb explodes and 3 pieces are flying in different directions.
Piece 1 : weighs 2kg and is traveling at the North East direction
Piece 2 : weighs 1kg and is traveling in the south direction ( exactly downards )
Piece 3 : weighs 3 kg and is traveling in the west direction ( exactly to the left )
Find the velocity and direction that Piece 1 is traveling 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?

 

[Phlogistonian]

You neglected to cancel out V1F in your final equations.

 

[Shin-]

No , i just rewrote it as Tanx V1f

Sinx/Cosx = Tanx ( trig identity )

 

[Shin-]

any ideas?

 

[alphysicist]

Hi Shin,

I think you misunderstood Phlogistonian's post.

You had:

Sinx V1F 15 m/s
--------- = -------
Cosx V1F 30 m/s

this simplifies to

tan x = (1/2)

The V1F is not inside the trig function and so will cancel since it is in both numerator and denominator.