Question

EL. A white ball with mass 143 g is moving at a velocity of 7.9 m/s.

CS
It collides with a red ball with mass of 150 g.
The red ball is stationary before the collision. The white ball stops after the collision.
Calculate the velocity of the red ball after the collision.
Give your answer to two significant figures.​

Answer 1

`\displaystyle v_2'=7.5\ m/s`

Step-by-step explanation:

Conservation Of Linear Momentum

The total momentum of both balls won't change regardless of their interaction while no external forces are acting on the system. We'll use the following variables m1,m2,v1,v2,v1',v2' for the mass of the white ball, the mass of the red ball, their velocities before the collision, and their velocities after the collision, respectively .

The provided data is as follows:

`\displaystyle m_1=143\ gr=0.143\ kg`

`\displaystyle v_1=7.9\ m/s`

`\displaystyle m_2=150\ gr=0.15\ kg`

`\displaystyle v_2=0`

`\displaystyle v_1'=0`

To preserve the total linear momentum, the following equation must stand

`\displaystyle m_1\ v_1+m_2\ v_2=m_1\ v_1'+m_2\ v_2'`

Solving for
`v_2'`

`\displaystyle v_2'=(m_1\ v_1+m_2\ v_2-m_1\ v_1')/(m_2)`

`\displaystyle v_2'=(0.143(7.9)+0-0)/(0.15)`

The final speed of the red ball is

`\boxed{\displaystyle v_2'=7.5\ m/s}`