Answer:
(a) 2.03 m/s
(b) 2.15 m/s
Explanation:
(a)
From the law of conservation of momentum, the sum of initial momentum equals the sum of final momentum
Momentum, p=mv where m is the mass and v is the velocity
[tex]m_1v_1+m_2v_2=(m_1+m_2)v_c[/tex] where [tex]v_c[/tex] is the common velocity, [tex]v_1[/tex] and [tex]v_2[/tex] are velocities of the first railroad car and the second railroad car respectively, [tex]m_1[/tex] and [tex]m_2[/tex] are masses of the first railroad car and the second railroad car respectively
Substituting the given figures then
[tex]21700\times 3.36+41700\times 1.34=(21700+41700)v_c\\63400v_c=128790\\v_c=\frac {128790}{63400}=2.031388013\approx 2.03 m/s[/tex]
(b)
Momentum, p=mv where m is the mass and v is the velocity
[tex]m_1v_1+m_2v_2=m_1v_3+m_2v_4[/tex] where [tex]v_1[/tex] and [tex]v_2[/tex] are initial velocities of the ball moving towards west and the other ball moving in opposite direction respectively, [tex]m_1[/tex] and [tex]m_2[/tex] are masses of the first railroad car and the second railroad car respectively
Taking west as positive then the opposite direction will be negative hence
[tex]0.455\times 7.36+(1.01\times -12.4)= 0.455\times -15.4 + (1.01\times v_4}[/tex]
Note that when the 0.455 rebounds, it moves towards East and since we took West as positive that is why we give 15.4 as a negative value.
[tex]-2.1682=1.01v_4\\v_4=\frac {-2.1682}{1.01}=-2.146732673\approx 2.15 m/s[/tex] towards East
