Answer :
Sure! Let's go through the steps to find the momentum of the man and the bike:
1. Identify the Given Information:
- Mass of the man, [tex]\( m_{\text{man}} = 90 \)[/tex] kg
- Mass of the bike, [tex]\( m_{\text{bike}} = 15 \)[/tex] kg
- Initial velocity, [tex]\( v_{\text{initial}} = 14 \)[/tex] m/s (to the right)
- Applied force, [tex]\( F = 159 \)[/tex] N (to the left)
- Time during which the force is applied, [tex]\( t = 2.5 \)[/tex] seconds
2. Calculate the Total Mass:
- Total mass, [tex]\( m_{\text{total}} = m_{\text{man}} + m_{\text{bike}} = 90 + 15 = 105 \)[/tex] kg
3. Calculate the Initial Momentum:
- Initial momentum [tex]\( p_{\text{initial}} = m_{\text{total}} \times v_{\text{initial}} = 105 \times 14 = 1470 \)[/tex] kg·m/s
4. Calculate the Acceleration:
- Acceleration can be found using the formula: [tex]\( \text{acceleration} = \frac{\text{force}}{\text{mass}} \)[/tex]
- So, [tex]\( a = \frac{159}{105} \approx 1.514 \, \text{m/s}^2 \)[/tex]
5. Determine the Change in Velocity:
- Change in velocity can be calculated as: [tex]\( \text{change in velocity} = \text{acceleration} \times \text{time} \)[/tex]
- As the force is applied to the left, the change in velocity is negative.
- [tex]\( \text{change in velocity} = 1.514 \times 2.5 \times -1 \approx -3.786 \, \text{m/s} \)[/tex]
6. Calculate the Final Velocity:
- Final velocity [tex]\( v_{\text{final}} = v_{\text{initial}} + \text{change in velocity} \)[/tex]
- [tex]\( v_{\text{final}} = 14 - 3.786 = 10.214 \, \text{m/s} \)[/tex]
7. Calculate the Final Momentum:
- Final momentum [tex]\( p_{\text{final}} = m_{\text{total}} \times v_{\text{final}} = 105 \times 10.214 \approx 1072.5 \)[/tex] kg·m/s
Therefore, the initial momentum of the man and the bike is 1470 kg·m/s, and the final momentum after the force is applied is approximately 1072.5 kg·m/s.
1. Identify the Given Information:
- Mass of the man, [tex]\( m_{\text{man}} = 90 \)[/tex] kg
- Mass of the bike, [tex]\( m_{\text{bike}} = 15 \)[/tex] kg
- Initial velocity, [tex]\( v_{\text{initial}} = 14 \)[/tex] m/s (to the right)
- Applied force, [tex]\( F = 159 \)[/tex] N (to the left)
- Time during which the force is applied, [tex]\( t = 2.5 \)[/tex] seconds
2. Calculate the Total Mass:
- Total mass, [tex]\( m_{\text{total}} = m_{\text{man}} + m_{\text{bike}} = 90 + 15 = 105 \)[/tex] kg
3. Calculate the Initial Momentum:
- Initial momentum [tex]\( p_{\text{initial}} = m_{\text{total}} \times v_{\text{initial}} = 105 \times 14 = 1470 \)[/tex] kg·m/s
4. Calculate the Acceleration:
- Acceleration can be found using the formula: [tex]\( \text{acceleration} = \frac{\text{force}}{\text{mass}} \)[/tex]
- So, [tex]\( a = \frac{159}{105} \approx 1.514 \, \text{m/s}^2 \)[/tex]
5. Determine the Change in Velocity:
- Change in velocity can be calculated as: [tex]\( \text{change in velocity} = \text{acceleration} \times \text{time} \)[/tex]
- As the force is applied to the left, the change in velocity is negative.
- [tex]\( \text{change in velocity} = 1.514 \times 2.5 \times -1 \approx -3.786 \, \text{m/s} \)[/tex]
6. Calculate the Final Velocity:
- Final velocity [tex]\( v_{\text{final}} = v_{\text{initial}} + \text{change in velocity} \)[/tex]
- [tex]\( v_{\text{final}} = 14 - 3.786 = 10.214 \, \text{m/s} \)[/tex]
7. Calculate the Final Momentum:
- Final momentum [tex]\( p_{\text{final}} = m_{\text{total}} \times v_{\text{final}} = 105 \times 10.214 \approx 1072.5 \)[/tex] kg·m/s
Therefore, the initial momentum of the man and the bike is 1470 kg·m/s, and the final momentum after the force is applied is approximately 1072.5 kg·m/s.
