Rocket Explosion Momentum Problem: Troubleshooting for EIT Review

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The discussion revolves around a rocket explosion problem involving two fragments, where the initial momentum is calculated as 6000 kgm/s. The user attempts to apply conservation of momentum to find the velocities of the fragments, resulting in incorrect values of Va and Vb. Despite solving the equations, the user believes the solutions manual may be incorrect as their calculations differ significantly from the expected answers. Other participants affirm the user's solution approach, indicating that the calculations appear correct. The thread highlights the challenges of troubleshooting momentum problems in preparation for the EIT review.
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Homework Statement



A rocket explodes into two fragments with the following information:

Initial trajectory: 150 m/s in the x-direction, mass is 40kg

Portion a, post explosion: 45 degree angle above the horizontal, 25kg

Portion b, post explosion: 30 degree angle below the horizontal, 15kg


Homework Equations



Conservation of momentum

The Attempt at a Solution



pi=150(m/s)*40kg=6000 kgm/s
pa=Va[cos 45, sin 45]*25kg=Va(17.68+17.68[j])kg
pb=Vb(cos 30, -sin 30[j])*15kg=Vb(12.99-7.5[j])kg

By conservation of momentum: pi=pa+pb

Two equations in two unknowns:

17.68*Va+12.99*Vb=6000
17.68*Va-7.5*Vb=0

Solving these gives me:

Va=124.2 m/s
Vb=292.8 m/s

However this is wrong, the answer should be:

Va=43.92 m/s
Vb=146.41 m/s

What am I doing wrong here? This is such a simple problem I am reviewing for the EIT, but I cannot for the life of me find out what's wrong and I am getting all the other momentum problems correct. Is the solutions manual incorrect?

Thank you in advance for the help!
 
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Your solution looks good to me.
 
I agree, your sol'n is correct.
 
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