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Sagot :
Answer:[tex]\begin{gathered} v_2=-(u_1+2v_1) \\ v_1=\frac{u_1-v_2}{2} \end{gathered}[/tex]Explanation:
Mass of object 1 = m₁
Velocity of object 1, = u₁
The mass of object 2 is half that of object 1
m₂ = m₁/2
The velocity of object 2 is three times the speed of object 1 but in the opposite direction
u₂ = -3u₁
The final velocity of both object is represented by v
Applying the principle of momentum conservation
[tex]\begin{gathered} m_1u_1+m_2u_2=m_1v_1+m_2v_2 \\ \\ m_1u_1+\frac{1}{2}m_1(-3u_1)=m_1v_1+\frac{1}{2}m_1v_2 \\ \\ m_1u_1-\frac{3(m_1u_1)}{2}=\frac{2m_1v_1+m_1v_2}{2} \\ \\ \frac{2m_1u_1-3m_1u_1}{2}=\frac{2m_1v_1+m_1v_2}{2} \\ \\ -m_1u_1=2m_1v_1+m_1v_2 \\ \\ m_1v_2=-m_1u_1-2m_1v_1 \\ \\ v_2=\frac{-m_1(u_1+2v_1)}{m_1} \\ \\ v_2=-(u_1+2v_1) \\ \\ \end{gathered}[/tex]From the last equation, make v₁ the subject of the formula instead
[tex]\begin{gathered} v_2=-(u_1+2v_1) \\ \\ v_2=-u_1-2v_1 \\ \\ 2v_1=u_1-v_2 \\ \\ v_1=\frac{u_1-v_2}{2} \\ \\ \end{gathered}[/tex]
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