Answer: The velocity of the cart-2 is 2 m/s moving in direction opposite of the cart-1's direction.
Explanation:
Mass of cart-1 ,[tex]m_1=10.0 kg[/tex]
Velocity of cart-1 before the release of the spring,[tex]u_1=0m/s[/tex]
Mass of cart-2 ,[tex]m_1=15kg[/tex]
Velocity of cart-2 before the release of the spring,[tex]u_2=0m/s[/tex]
After releasing of the spring:
Velocity of cart-1 after the release of the spring,[tex]v_1=3 m/s[/tex]
Velocity of cart-2 after the release of the spring,[tex]v_2=?[/tex]
According to law of conservation of momentum:
[tex]m_1u_1+m_2u_2=m_2v_2+m_2v_2[/tex]
[tex]10.0 kg\times 0m/s+15 kg\times 0 m/s=10.0 kg\times 3m/s+15v_2[/tex]
[tex]0+0=30 kg m/s+15 mv_2[/tex]
[tex]v_2=-2 m/s[/tex]
Negative sign depicts that direction of cart-2 which is moving in the opposite direction of the cart-1's direction. So, the velocity of the cart 2 is 2 m/s.
