The final speed of the combination of brick and cart is 15.1 m/s
Explanation:
We can solve this problem by using the law of conservation of momentum: in absence of external forces, the total momentum of the brick+cart must be conserved before and after the moment the brick is placed on the cart.
Mathematically:
[tex]p_i = p_f\\m_1 u_1 + m_2 u_2 = (m_1+m_2)v[/tex]
where:
[tex]m_1 = 2.1 kg[/tex] is the mass of the brick
[tex]u_1 = 0[/tex] is the initial velocity of the brick (we can assume it is at rest)
[tex]m_2 = 2.9 kg[/tex] is the mass of the cart
[tex]u_2 = 26 m/s[/tex] is the initial velocity of the cart
[tex]v[/tex] is the final combined velocity of the cart+brick
Solving the equation for v, we find the final velocity of the system:
[tex]v=\frac{m_1 u_1 + m_2 u_2}{m_1+m_2}=\frac{0+(2.9)(26)}{2.1+2.9}=15.1 m/s[/tex]
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