(adsbygoogle = window.adsbygoogle || []).push({}); [solved] resulting velocity of 2 particles

1. The problem statement, all variables and given/known data

2. Relevant equations

conservation of momentum

[tex]m_Av_A'=m_Bv_B'[/tex]

[tex]v_A'=\frac{m_B}{m_A}v_B'[/tex]

conservation of energy

[tex]V=\frac{1}{2}m_A(v_A')^2+\frac{1}{2}m_B(v_B')^2=\frac{1}{2}m_A\left(\frac{m_B}{m_A}v_B'\right)^2+\frac{1}{2}m_B(v_B')^2[/tex]

[tex]v_B'=\sqrt{\frac{2m_AV}{m_B(m_A+m_B)}}[/tex]

3. The attempt at a solution

[tex]m_A=0.9Kg[/tex]

[tex]m_B=1.35Kg[/tex]

[tex]V=1.35Nm[/tex]

[tex]v_B'=\sqrt{\frac{2\cdot0.9\cdot1.35}{1.35(0.9+1.35)}}=\sqrt{0.8}\approx{0.8944[m/s]}[/tex]

[tex]v_A'=\frac{1.35}{0.9}\cdot0.8944=1.3416[m/s][/tex]

from the law of cosines

[tex]v_B=\sqrt{6^2+0.8944^2-2\cdot6\cdot0.8944\cdot\cos{60^o}}\approx5.607[m/s][/tex]

from the law of sines

[tex]\sin{\beta}=\frac{\sin{60^o}\cdot0.8944}{5.607}\approx0.1381[/tex]

[tex]\beta\approx7.94^o[/tex]

As you can see that result is totally different from the solution given by my teacher. I also get different results for the other velocity. So either my calculations are incorrect or my teacher gave us wrong results. I'll be grateful for any help, thank you.

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# Homework Help: Resulting velocity of 2 particles

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