### Physics Problem: Conservation of Momentum #### Problem Statement:A **72-kg fisherman** in a **138-kg boat** throws a package of mass **m = 15 kg** horizontally toward the right with a speed of **vᵢ = 4.7 m/s**, as shown in the figure below. Neglecting water resistance, and assuming the boat is at rest before the package is thrown, find the velocity of the boat after the package is thrown.#### Given Data:- Mass of fisherman (m₁): 72 kg- Mass of boat (m₂): 138 kg- Mass of package (m): 15 kg- Initial speed of package (vᵢ): 4.7 m/s (to the right)#### Diagram Description:The diagram shows a man in a boat on a body of water. The man is throwing a package horizontally towards the right. An arrow pointing to the right represents the velocity of the package after it is thrown.1. **Figure Explanation:** - The fisherman is on the left side of the boat. - The package is shown with an arrow indicating its motion to the right with velocity vᵢ. - The boat is initially at rest before the package is thrown into the water. 2. **Mathematical Formulation (Applying Conservation of Momentum):**Since there is no external force acting on the system (fisherman, boat, and package), the total momentum before and after the package is thrown must be equal.\[ m*vᵢ = (m₁ + m₂) \cdot v_b \]Where:- $ m $ is the mass of the package- $ vᵢ $ is the initial speed of the package- $ m₁ $ and $ m₂ $ are the masses of the fisherman and the boat respectively- $ v_b $ is the velocity of the boat (including the fisherman) after the package is thrown#### Calculation:Substitute the given values into the conservation of momentum equation:\[ 15 \text{ kg} * 4.7 \text{ m/s} = (72 \text{ kg} + 138 \text{ kg}) * v_b \]\[ 70.5 \text{ kg·m/s} = 210 \text{ kg} * v_b \]Solve for \( v_b

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Description: ### Physics Problem: Conservation of Momentum #### Problem Statement:A **72-kg fisherman** in a **138-kg boat** throws a package of mass **m = 15 kg** horizontally toward the right with a speed of **vᵢ = 4.7 m/s**, as shown in the figure below. Negl

Given: mass of fishermen = 72 kg mass of boat = 138 kg mass of package, m = 15 kg speed of package,…

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A 72-kg fisherman in a 138-kg boat throws a package of mass m = 15 kg horizontally toward the right with a speed of v, = 4.7 m/s as in the figure below. Neglecting water resistance, and assuming the boat is at rest before the package is thrown, find the velocity of the boat after the package is thrown. magnitude Your response is off by a multiple of ten. m/s toward the left direction

A 72-kg fisherman in a 138-kg boat throws a package of mass m = 15 kg horizontally toward the right with a speed of v, = 4.7 m/s as in the figure below. Neglecting water resistance, and assuming the boat is at rest before the package is thrown, find the velocity of the boat after the package is thrown. magnitude Your response is off by a multiple of ten. m/s toward the left direction

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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### Physics Problem: Conservation of Momentum

#### Problem Statement:
A **72-kg fisherman** in a **138-kg boat** throws a package of mass **m = 15 kg** horizontally toward the right with a speed of **vᵢ = 4.7 m/s**, as shown in the figure below. Neglecting water resistance, and assuming the boat is at rest before the package is thrown, find the velocity of the boat after the package is thrown.

#### Given Data:
- Mass of fisherman (m₁): 72 kg
- Mass of boat (m₂): 138 kg
- Mass of package (m): 15 kg
- Initial speed of package (vᵢ): 4.7 m/s (to the right)

#### Diagram Description:
The diagram shows a man in a boat on a body of water. The man is throwing a package horizontally towards the right. An arrow pointing to the right represents the velocity of the package after it is thrown.

1. **Figure Explanation:**
- The fisherman is on the left side of the boat.
- The package is shown with an arrow indicating its motion to the right with velocity vᵢ.
- The boat is initially at rest before the package is thrown into the water.

2. **Mathematical Formulation (Applying Conservation of Momentum):**

Since there is no external force acting on the system (fisherman, boat, and package), the total momentum before and after the package is thrown must be equal.

\[ m*vᵢ = (m₁ + m₂) \cdot v_b \]

Where:
- $ m $ is the mass of the package
- $ vᵢ $ is the initial speed of the package
- $ m₁ $ and $ m₂ $ are the masses of the fisherman and the boat respectively
- $ v_b $ is the velocity of the boat (including the fisherman) after the package is thrown

#### Calculation:
Substitute the given values into the conservation of momentum equation:

\[ 15 \text{ kg} * 4.7 \text{ m/s} = (72 \text{ kg} + 138 \text{ kg}) * v_b \]

\[ 70.5 \text{ kg·m/s} = 210 \text{ kg} * v_b \]

Solve for \( v_b

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