The question is confusing for the initial direction of the green ball. We assume to the left.
Answer:
The mass of the green ball is 360 Kg
Explanation:
Law Of Conservation Of Linear Momentum
The total momentum of a system of bodies is conserved unless an external force is applied to it. The formula for the momentum of a body with mass m and velocity v is
P=mv.
If we have a system of bodies, then the total momentum is the sum of the individual momentums
[tex]P=m_1v_1+m_2v_2+...+m_nv_n[/tex]
If some collision occurs, the velocities change to v' and the final momentum is:
[tex]P'=m_1v'_1+m_2v'_2+...+m_nv'_n[/tex]
In a system of two masses, the law of conservation of linear momentum
is written as:
[tex]m_1v_1+m_2v_2=m_1v'_1+m_2v'_2[/tex]
Let's call m1=30 Kg the mass of the red ball moving to the right at v1=4 m/s, m2 (unknown) the mass of the green ball moving at v2=-5 m/s to the left (assumed).
After the collision, the red ball rolls to the left at v1'=-2 m/s and the green ball is at v2'=-4.5 m/s. Thus:
[tex]30*4+m_2*(-5)=30*(-2)+m_2(-4.5)[/tex]
Operating:
[tex]120-5m_2=-60-4.5m_2[/tex]
[tex]120+60=5m_2-4.5m_2[/tex]
[tex]180=0.5m_2[/tex]
[tex]m_2=180/0.5=360[/tex]
The mass of the green ball is 360 Kg
