Given:
The mass of the locomotive is m1 = 110000 kg
The initial speed of the locomotive is
[tex]v_{initial}=\text{ 1 m/s}[/tex]The mass of the rail car is m2 = 25000 kg
The initial speed of the rail car is zero.
The radius of the wheel is r = 0.48 m
To find
The final velocity of the locomotive and the car.
The angular velocity after collision.
Explanation:
The final velocity can be calculated as
[tex]\begin{gathered} m1v_{initial}+m2\times0=(m1+m2)v_{final} \\ v_{final}=\frac{m1v_{initial}}{m1+m2} \\ =\frac{110000\times1}{110000+25000} \\ =\text{ 0.82 m/s} \end{gathered}[/tex]The angular velocity after the collision can be calculated as
[tex]\begin{gathered} \omega=\frac{v_{final}}{r} \\ =\frac{0.82}{0.48} \\ =1.7\text{ rad/s} \end{gathered}[/tex]