Question

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Answer 1

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 momentum of a body with mass m and velocity v is calculated as follows:

P=mv

If we have a system of masses, then the total momentum is the sum of all the individual momentums:

$P=m_1v_1+m_2v_2+...+m_nv_n$

When a collision occurs, the velocities change to v' and the final momentum is:

$P'=m_1v'_1+m_2v'_2+...+m_nv'_n$

In a system of two masses, the law of conservation of linear momentum is simplified to:

$m_1v_1+m_2v_2=m_1v'_1+m_2v'_2$

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 comes to rest v2'=0. It's required to find the final speed v1' after the collision.

The above equation is solved for v1':

$\displaystyle v'_1=\frac{m_1v_1+m_2v_2-m_2v'_2}{m_1}$

$\displaystyle v'_1=\frac{0.16*0+0.17*2-0.17*0}{0.16}$

$\displaystyle v'_1=\frac{0.34}{0.16}$

$v'_1=2.125\ m/s$

The speed of the 8-ball is 2.125 m/s after the collision.