To solve this problem it is necessary to apply the concepts related to the conservation of the momentum for an inelastic shock. Mathematically this can be described as
[tex]m_1v_1 + m_2v_2 = (m_1+m_2)V_f[/tex]
Where,
m_{1,2} = Mass of each object
v_{1,2} = Initial velocity of each object
V_f = Final Velocity
If we assign the value of mass 1 and speed 1 to the cart and the variable of mass 2 to clay (which is at rest) we will have:
[tex]m_1v_1 + m_2v_2 = (m_1+m_2)V_f[/tex]
[tex](306)(14.2) + (76.3)(0) = (306+76.3)V_f[/tex]
[tex]V_f = 11.36cm/s[/tex]
Therefore the final speed of the system would be 11.36cm/s
