This question involves the concept of the law of conservation of momentum.
The velocity of the 8 kg cart after the collision is "4 m/s left direction".
LAW OF CONSERVATION OF MOMENTUM
According to the law of conservation of momentum, the total momentum of an isolated system before and after the collision remains constant.
[tex]m_1u_1+m_2u_2=m_1v_1+m_2v_2[/tex]
where,
- m₁ = mass of first cart = 8 kg
- m₂ = mass of second cart = 4 kg
- u₁ = velocity of 8 kg cart before collision = 4 m/s
- u₂ = mass of 4 kg cart before collision = - 6 m/s
- v₁ = velocity of 8 kg cart after collision =?
- v₂ = mass of 4 kg cart after collision = 3 m/s
Taking the right side as the positive direction and the left side as the negative direction.
Therefore,
[tex](8\ kg)(4\ m/s)+(4\ kg)(-6\ m/s)=(8\ kg)(v_1)+(4\ kg)(3\ m/s)\\\\v_1=\frac{32\ kg.m/s-24\ kg.m/s-12\ kg.m/s}{8\ kg}[/tex]
v₁ = - 4 m/s
negative sign shows left direction.
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