The final speed of the cart and the bag is 2.2 m/s
Explanation:
We can solve this problem by using the law of conservation of momentum: in fact, in absence of external forces, the total momentum of the bag and the cart must be conserved before and after the collision.
Mathematically:
[tex]p_i = p_f\\m_1 u_1 + m_2 u_2 = (m_1+m_2)v[/tex]
where:
[tex]m_1 = 9.4 kg[/tex] is the mass of the bag of rice
[tex]u_1 = 7.0 m/s[/tex] is the initial velocity of the bag
[tex]m_2 = 19.9 kg[/tex] is the mass of the cart
[tex]u_2 =0 m/s[/tex] is the initial velocity of the cart (at rest)
[tex]v[/tex] is the final combined velocity of the bag and the cart
Re-arranging the equation and solving for v, we find:
[tex]v=\frac{m_1 u_1 + m_2 u_2}{m_1+m_2}=\frac{(9.4)(7.0)+0}{9.4+19.9}=2.2 m/s[/tex]
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