Answer:
The speed of the 8-ball is 2.125 m/s after the collision.
Explanation:
Law Of Conservation Of Linear Momentum
The total momentum of a system of masses is conserved unless an external force is applied. The formula for the momentum of a body with mass m and velocity v is
P=mv
If we have a system of masses, then the total momentum is the sum of them all
[tex]P=m_1v_1+m_2v_2+...+m_nv_n[/tex]
If a 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 takes the form:
[tex]m_1v_1+m_2v_2=m_1v'_1+m_2v'_2[/tex]
The m1=0.16 Kg 8-ball is initially at rest v1=0. It is hit by an m2=0.17 Kg cue ball that was moving at v2=2 m/s.
After the collision, the cue ball remains at rest v2'=0. It's required to find the final speed v1' after the collision.
The last equation is solved for v1':
[tex]\displaystyle v'_1=\frac{m_1v_1+m_2v_2-m_2v'_2}{m_1}[/tex]
[tex]\displaystyle v'_1=\frac{0.16*0+0.17*2-0.17*0}{0.16}[/tex]
[tex]\displaystyle v'_1=\frac{0.34}{0.16}[/tex]
[tex]v'_1=2.125\ m/s[/tex]
The speed of the 8-ball is 2.125 m/s after the collision.
