Rocket Explosion Momentum Problem: Troubleshooting for EIT Review

[cmmcnamara]

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!

 

[voko]

Your solution looks good to me.

 

[rude man]

I agree, your sol'n is correct.