Given that the mass of toy car is, m = 1.45 kg and the mass of toy train is, M = 3.85 m/s.
The initial velocity of the toy train is u_t = 2.05 m/s.
The initial velocity of the toy car is u_c = 4.75 m/s
After the collision, the final velocity of the toy car is v_c = 2.05 m/s
(a) The final velocity of the toy train can be obtained using the conservation of momentum,
[tex]\begin{gathered} mu_{_c}+Mu_t_{}=mv_c+Mv_{_t} \\ v_t=\frac{mu_c+Mu_t-mv_c}{M} \\ =\frac{11.8075}{3.85} \\ =3.06\text{ m/s} \end{gathered}[/tex]
(b) Initial kinetic energy is
[tex]\begin{gathered} KE._i=\frac{1}{2}m(u_c)^2+\frac{1}{2}M(u_t)^2 \\ =\frac{1}{2}1.45(4.75)^2+\frac{1}{2}3.85(2.05)^2 \\ =24.4476\text{ J} \end{gathered}[/tex]
Final kinetic energy is
[tex]\begin{gathered} KE._f=\frac{1}{2}m(v_c)^2+\frac{1}{2}M(v_t)^2 \\ =\frac{1}{2}1.45(2.05)^2+\frac{1}{2}3.85(3.06)^2 \\ =21.0717\text{ J} \end{gathered}[/tex]
Thus, a change in kinetic energy will be
[tex]\begin{gathered} \Delta KE=KE._f-K.E._i \\ =21.06-24.43 \\ =-3.3759\text{ J} \end{gathered}[/tex]
