Respuesta :
Given data
*The given mass of the empty freight car is m_1 = m
*The given initial speed of the empty freight car is v_1 = 1.20 m/s
*The mass of the fully loaded boxcar is m_2 = 5.20 m
*The initial speed of the fully loaded boxcar is v_2 = 0 m/s
(A)
The formula for the speed of the two cars after the collision is given by the conservation of momentum as
[tex]\begin{gathered} P_i=P_f \\ m_1v_1+m_2v_2=(m_1+m_2)v_{} \\ v=\frac{m_1v_1+m_2v_2}{(m_1+m_2)} \end{gathered}[/tex]Substitute the known values in the above expression as
[tex]\begin{gathered} v=\frac{(m)(1.20)+(5.20m)(0)}{(m+5.20m)} \\ =0.19\text{ m/s} \end{gathered}[/tex]Hence, the speed of the two cars after the collision is v = 0.19 m/s
(B)
As from the given data, the two cars are at rest after the collision. It means the final speed of the two cars equals to zero (v_f = 0 m/s).
The formula for the speed of the loaded box car before the collision is given by the conservation of momentum as
[tex]\begin{gathered} p_i=p_f \\ m_1v_1+m_2v_l=(m_1+m_2)v_f \end{gathered}[/tex]Substitute the known values in the above expression as
[tex]\begin{gathered} m(1.20)+(5.20m)(v_l)=(m+5.20m)(0)_{} \\ v_l=-\frac{1.20m}{5.20m} \\ =-0.23\text{ m/s} \end{gathered}[/tex]