Rocket: conservation of momentum

[Np14]

Homework Statement

A fireworks rocket is moving at a speed of 45.0 m/s. The rocket suddenly breaks into two pieces of equal mass, which fly off with velocities v₁ and v₂. What are the magnitudes of v₁ and v₂?

Homework Equations

Conservation of Momentum
m₁v₁ + m₂v₂ = m₁v_o1 + m₂v_o2

The Attempt at a Solution

v₁ = 45cos30° = 38.97
v₂ = 45cos60° = 22.55

45 m/s ≠ 61.47 m/s

I have a feeling this problem is a lot more complicated, but I am not sure how to solve it.

 

[phinds]

Homework Statement

A fireworks rocket is moving at a speed of 45.0 m/s. The rocket suddenly breaks into two pieces of equal mass, which fly off with velocities v₁ and v₂. What are the magnitudes of v₁ and v₂?

Homework Equations

Conservation of Momentum
m₁v₁ + m₂v₂ = m₁v_o1 + m₂v_o2

The Attempt at a Solution

v₁ = 45cos30° = 38.97
v₂ = 45cos60° = 22.55

45 m/s ≠ 61.47 m/s

I have a feeling this problem is a lot more complicated, but I am not sure how to solve it.

Your problem statement makes no mention of 30 and 60 degrees yet you introduce them in your solution. I think you should draw a diagram and do a better job of stating the problem.

 

[rude man]

Answer depends on what caused the rocket to break up. If it was an internal explosion then the answer depends on how severe the explosion was. If it just broke in two, what would v1 and v2 be?

 

[haruspex]

have a feeling this problem is a lot more complicated

Yes, your method has no logic to it. Why should the speeds be given by those expressions?
Use the conservation equation you quoted, once in the original direction and once at right angles to that.

 

[neilparker62]

Homework Statement

A fireworks rocket is moving at a speed of 45.0 m/s. The rocket suddenly breaks into two pieces of equal mass, which fly off with velocities v₁ and v₂. What are the magnitudes of v₁ and v₂?

Homework Equations

Conservation of Momentum
m₁v₁ + m₂v₂ = m₁v_o1 + m₂v_o2

The Attempt at a Solution

v₁ = 45cos30° = 38.97
v₂ = 45cos60° = 22.55

p₁ = 2m x 45 cos30° = 2m x 38.97
p₂ = 2m x 45 cos60° = 2m x 22.55

45 m/s ≠ 61.47 m/s

I have a feeling this problem is a lot more complicated, but I am not sure how to solve it.