The final velocity of the two carts is 0.51 m/s
Explanation:
We can solve the problem by using the law of conservation of momentum: in fact, the total momentum of the two carts must be conserved before and after the collision, in absence of external forces. Thus, we can write:
[tex]p_i = p_f\\m_1 u_1 + m_2 u_2 = (m_1+m_2)v[/tex]
where:
[tex]m_1 = 0.180 kg[/tex] is the mass of the first cart
[tex]u_1 = 0.80 m/s[/tex] is the initial velocity of the first cart
[tex]m_2 = 0.100 kg[/tex] is the mass of the second cart
[tex]u_2 = 0[/tex] is the initial velocity of the second cart (at rest)
[tex]v[/tex] is the final combined velocity of the two carts
Re-arranging the equation and substituting the values, we find the final velocity of the two carts after the collision:
[tex]v=\frac{m_1 u_1 + m_2 u_2}{m_1+m_2}=\frac{(0.180)(0.80)+0}{0.180+0.100}=0.51 m/s[/tex]
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