To determine the velocity of the 5 kg ball after the collision, we can use the principle of conservation of momentum.
### Step-by-Step Solution:
1. Identify Initial Conditions:
- The 5 kg ball is stationary initially, so its initial velocity [tex]\( u_1 = 0 \, \text{m/s} \)[/tex].
- The question does not mention the initial velocity of the 10 kg ball explicitly. For this solution, we'll assume that the 10 kg ball is also initially stationary, so [tex]\( u_2 = 0 \, \text{m/s} \)[/tex].
2. Identify Final Conditions:
- After the collision, the 10 kg ball is moving in the same direction with a velocity of [tex]\( v_2 = 5 \, \text{m/s} \)[/tex].
3. Identify Masses:
- Mass of the first ball (5 kg ball), [tex]\( m_1 = 5 \, \text{kg} \)[/tex].
- Mass of the second ball (10 kg ball), [tex]\( m_2 = 10 \, \text{kg} \)[/tex].
4. Apply the Law of Conservation of Momentum:
- According to the conservation of momentum, the total momentum before the collision equals the total momentum after the collision.
- Therefore:
[tex]\[
m_1 u_1 + m_2 u_2 = m_1 v_1 + m_2 v_2
\][/tex]
Where:
[tex]\[ u_1 = 0 \, \text{m/s}, \quad u_2 = 0 \, \text{m/s}, \quad v_2 = 5 \, \text{m/s} \][/tex]
5. Simplify the Equation:
- Plugging in the initial velocities and masses:
[tex]\[
5 \cdot 0 + 10 \cdot 0 = 5 v_1 + 10 \cdot 5
\][/tex]
This simplifies to:
[tex]\[
0 = 5 v_1 + 50
\][/tex]
6. Solve for the Final Velocity of the 5 kg Ball ( [tex]\( v_1 \)[/tex] ):
- Isolating [tex]\( v_1 \)[/tex]:
[tex]\[
5 v_1 = -50
\][/tex]
[tex]\[
v_1 = \frac{-50}{5}
\][/tex]
[tex]\[
v_1 = -10 \, \text{m/s}
\][/tex]
### Conclusion:
The velocity of the 5 kg ball after the collision is [tex]\( -10 \, \text{m/s} \)[/tex]. This negative sign indicates that the 5 kg ball is moving in the direction opposite to the initial direction of the 10 kg ball.
