The final speed of the cart and the bag is 1.9 m/s
Explanation:
We can solve the problem by using the law of conservation of momentum: in fact, in absence of external forces, the total momentum of the system must be conserved before and after the collision.
Therefore, 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 = 8.9 kg[/tex] is the mass of the bag
[tex]u_1 = 5.7 m/s[/tex] is the initial velocity of the bag
[tex]m_2 = 18.4 kg[/tex] is the mass of the cart
[tex]u_2 = 0[/tex] is the initial velocity of the cart (which is stationary)
[tex]v[/tex] is the final combined velocity of the cart with the bag
Re-arranging the equation and substituting, we find the final combined velocity (and speed):
[tex]v=\frac{m_1 u_1 + m_2 u_2}{m_1+m_2}=\frac{(8.9)(5.7)+0}{8.9+18.4}=1.9 m/s[/tex]
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