Math Problem Statement
Solution
This problem involves a system where a football player throws a football while moving on smooth ice. To solve this, we apply the principle of conservation of momentum.
Part A: Player's speed after throwing the ball at 15.5 m/s relative to the ground
Step-by-step solution:
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Initial conditions: The total momentum of the system (player + football) before the throw is the momentum of the player since the ball is being carried by him.
- Mass of the player =
- Mass of the football =
- Initial velocity of both player and football =
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Final conditions:
- After the throw, the football moves at relative to the ground.
- The player's velocity will change to , which we need to find.
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Conservation of momentum: Since no external forces act on the system, the total momentum before and after the throw must be the same.
Initial momentum:
Final momentum:
Using the conservation of momentum equation:
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Solve for :
Substitute the given values:
So, the player's speed after the throw is approximately 1.66 m/s.
Let me know if you'd like further details or explanations. Here are a few additional questions related to this topic:
- What is the direction of the player's velocity after the throw relative to the initial velocity?
- How does the mass of the football influence the player's final velocity?
- What if the football was thrown in the opposite direction of the player's motion? How would that affect the final velocity?
- How does the conservation of momentum principle apply in collisions?
- What external forces would violate the conservation of momentum in this scenario?
Tip: Always ensure the system is isolated when applying the conservation of momentum, meaning no external forces (like friction) are acting on it.
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Math Problem Analysis
Mathematical Concepts
Conservation of Momentum
Kinematics
System of Particles
Formulas
Initial momentum: p_i = (m_p + m_b) * v_i
Final momentum: p_f = m_p * v_f + m_b * v_b
Conservation of momentum: (m_p + m_b) * v_i = m_p * v_f + m_b * v_b
Theorems
Principle of Conservation of Momentum
Suitable Grade Level
Grades 10-12
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