Respuesta :
Explanation:
Mass of ball A, [tex]m_A=7\ kg[/tex]
Mass of ball B, [tex]m_B=3\ kg[/tex]
Initial velocity of ball A, [tex]u_A=12\ m/s[/tex]
Initial velocity of ball B, [tex]u_B=-1\ m/s[/tex]
We need to find the final velocity of each ball. For a perfectly elastic collision, the coefficient of restitution is equal to 1. It is given by :
[tex]e=\dfrac{v_B-v_A}{u_A-u_B}[/tex]
[tex]v_A\ and\ v_B[/tex] are final velocities of ball A and B
[tex]1=\dfrac{v_B-v_A}{13}[/tex]
[tex]v_B-v_A=13[/tex]...........(1)
Using the conservation of linear momentum as :
[tex]m_Au_A+m_Bu_B=m_Av_A+m_Bu_B[/tex]
[tex]7(12)+3(-1)=7v_A+3u_B[/tex]
[tex]7v_A+3u_B=81[/tex]..............(2)
On solving equation (1) and (2) using calculator we get :
[tex]v_A=4.2\ m/s[/tex]
[tex]v_B=17.2\ m/s[/tex]
So, the final velocities of ball A and B are 4.2 m/s and 17.2 m/s. Hence, this is the required solution.
