Given data
*The mass of cart 1 is 2.5 kg
*The mass of cart 2 is 4 kg
*The speed of the cart 1 before the collision is 5 m/s
*The speed of the cart 2 before the collision is -1.5 m/s
*The speed of the cart 2 after the collision is 3 m/s
The formula for the velocity of the cart 1 is given by the conservation of momentum as
[tex]\begin{gathered} P_i=P_f \\ m_1u_1+m_2u_{2_{}}=m_1v_1+m_2v_2 \end{gathered}[/tex]Substitute the known values in the above expression as
[tex]\begin{gathered} 2.5\times5+4\times-1.5=2.5\times v_1+4\times3_{} \\ 6.5=2.5v_1+12 \\ v_1=-2.2\text{ m/s} \end{gathered}[/tex]Thus, the velocity of Cart 1 after the collision is -2.2 m/s and the correct answer is (C)
