### Transcription and Explanation for an Educational Website---**Scenario:**Vahé and Nicolás, both with mass \( M \), are playing catch with a football of mass \( m \) on the frictionless surface of a frozen pond. Since they’re physics professors and not professional football players, they can only throw the football with a speed \( v_0 \) relative to themselves. **Question:**All of your answers below should be only in terms of \( m \), \( M \), and \( v_0 \).---#### (a) Momentum Conservation During Throw- **Situation:** Vahé throws the ball to his right toward Nicolás.- **Problem Statement:** Relative to a stationary observer on the surface of the pond, what is the speed \( v_1 \) with which the football is moving after it is thrown?**Diagram Explaining Momentum Conservation:**A diagram shows Vahé labeled \( V \) on the left with mass \( M \) throwing a football (mass \( m \)) to the right. The football moves with speed \( v_1 \) towards Nicolás, who is labeled \( N \) and also has mass \( M \).---#### (b) Motion After Catch- **Situation:** Nicolás catches the ball.- **Problem Statement:** What is the speed \( v_2 \) with which Nicolás and the ball are moving after he catches the ball?**Understanding the Diagram:**- **Initial Conditions:** Both individuals are stationary relative to each other initially.- **Post-Throw Process:** When Vahé throws the ball with speed \( v_0 \), momentum must be conserved in the system.- **After Catch:** Nicolás catches the ball, and the system's total momentum is conserved.---**Considerations for Each Part:**- Analyze the system using momentum conservation principles, considering the initial and final momentum states.- The frictionless surface means no external horizontal forces are acting on Vahé, Nicolás, or the ball.---By exploring the interactions and applying conservation laws, learners can derive expressions for \( v_1 \) and \( v_2 \) based on the given variables \( m \), \( M \), and \( v_0 \). This activity demonstrates the importance of momentum conservation in isolated systems.

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Description: ### Transcription and Explanation for an Educational Website---**Scenario:**Vahé and Nicolás, both with mass \( M \), are playing catch with a football of mass \( m \) on the frictionless surface of a frozen pond. Since they’re physics professors an

By using law of conservation of momentum

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Vahé and Nicolás, both with mass M, are playing catch with a football of mass m on the frictionless surface of a frozen pond. Since they're physics professors and not professional football players, they can only throw the football with a speed vo relative to themselves. All of your answers below should be only in terms of m, M, and vo- (a) Relative to a stationary observer on the surface of the pond, what is the speed v, with which the football is moving after it is Vahé throws the ball to his right, toward Nicolás. M thrown? (b) Nicolás catches the ball. What is the speed v2 with which Nicolás and the ball are moving after he catches the ball?

Vahé and Nicolás, both with mass M, are playing catch with a football of mass m on the frictionless surface of a frozen pond. Since they're physics professors and not professional football players, they can only throw the football with a speed vo relative to themselves. All of your answers below should be only in terms of m, M, and vo- (a) Relative to a stationary observer on the surface of the pond, what is the speed v, with which the football is moving after it is Vahé throws the ball to his right, toward Nicolás. M thrown? (b) Nicolás catches the ball. What is the speed v2 with which Nicolás and the ball are moving after he catches the ball?

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Question

### Transcription and Explanation for an Educational Website

---

**Scenario:**

Vahé and Nicolás, both with mass \( M \), are playing catch with a football of mass \( m \) on the frictionless surface of a frozen pond. Since they’re physics professors and not professional football players, they can only throw the football with a speed \( v_0 \) relative to themselves.

**Question:**
All of your answers below should be only in terms of \( m \), \( M \), and \( v_0 \).

---

#### (a) Momentum Conservation During Throw

- **Situation:** Vahé throws the ball to his right toward Nicolás.
- **Problem Statement:** Relative to a stationary observer on the surface of the pond, what is the speed \( v_1 \) with which the football is moving after it is thrown?

**Diagram Explaining Momentum Conservation:**

A diagram shows Vahé labeled \( V \) on the left with mass \( M \) throwing a football (mass \( m \)) to the right. The football moves with speed \( v_1 \) towards Nicolás, who is labeled \( N \) and also has mass \( M \).

---

#### (b) Motion After Catch

- **Situation:** Nicolás catches the ball.
- **Problem Statement:** What is the speed \( v_2 \) with which Nicolás and the ball are moving after he catches the ball?

**Understanding the Diagram:**

- **Initial Conditions:** Both individuals are stationary relative to each other initially.
- **Post-Throw Process:** When Vahé throws the ball with speed \( v_0 \), momentum must be conserved in the system.
- **After Catch:** Nicolás catches the ball, and the system's total momentum is conserved.

---

**Considerations for Each Part:**

- Analyze the system using momentum conservation principles, considering the initial and final momentum states.
- The frictionless surface means no external horizontal forces are acting on Vahé, Nicolás, or the ball.

---

By exploring the interactions and applying conservation laws, learners can derive expressions for \( v_1 \) and \( v_2 \) based on the given variables \( m \), \( M \), and \( v_0 \). This activity demonstrates the importance of momentum conservation in isolated systems.

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