Answer:
31 cm/s
Explanation:
Let's solve the problem by using conservation of momentum:
[tex]m_1 u_1 + m_2 u_2 = m_1 v_1 + m_2 v_2[/tex]
where:
[tex]m_1 = 3.5 g[/tex] is the mass of the blue marble
[tex]m_2=1.2 g[/tex] is the mass of the red marble
[tex]u_1 = 15 cm/s[/tex] is the initial velocity of the blue marble
[tex]u_2 = 3.5 cm/s[/tex] is the initial velocity of the red marble
[tex]v_1 = 5.5 cm/s[/tex] is the final velocity of the blue marble
We can find the final velocity of the red marble by re-arranging the equation and solving for [tex]v_2[/tex]:
[tex]v_2 = \frac{1}{m_2}(m_1 u_1 + m_2 u_2 - m_1 v_1)=[/tex]
[tex]=\frac{1}{1.2}(3.5\cdot 15 + 1.2 \cdot 3.5 - 3.5 \cdot 5.5 )=31 cm/s[/tex]
