2. Suppose a person on mass m = 75 (kg) is standing on the left end of a uniform boat of mass M = 200 (kg) and length L = 5 (m), as shown in the sketch. The boat is on the water, which for our purposes we will consider frictionless. When the person is standing on the left end of the boat (you can consider the person to be a point particle), the left end of the boat is at x = 0 (m). А. Where is the center of mass in x of the man-boat M system? Now suppose the man walks to the right hand edge of the boat. What is the x-coordinate of the left hand edge В. of the boat? С. After the man arrives at the right hand side of the boat (the man and boat are at rest), he jumps off horizontally (to the right) with speed v = 10 (m/s). What is the speed of the boat? (Magnitude and direction). D. What is the change in kinetic energy of the man-boat system between the time he was standing at rest on the right side of the boat to the time he immediately jumped off? Where did that energy come from (provide a brief answer)?

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Chapter1: Units, Trigonometry. And Vectors
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## Problem 2

Suppose a person of mass \( m = 75 \) kg is standing on the left end of a uniform boat of mass \( M = 200 \) kg and length \( L = 5 \) m, as shown in the sketch. The boat is on the water, which for our purposes we will consider frictionless. When the person is standing on the left end of the boat (you can consider the person to be a point particle), the left end of the boat is at \( x = 0 \) m.

### A. Where is the center of mass in \( x \) of the man-boat system?

### B. Now suppose the man walks to the right-hand edge of the boat. What is the \( x \)-coordinate of the left-hand edge of the boat?

### C. After the man arrives at the right-hand side of the boat (the man and boat are at rest), he jumps off horizontally (to the right) with speed \( v = 10 \) m/s. What is the speed of the boat? (Magnitude and direction).

### D. What is the change in kinetic energy of the man-boat system between the time he was standing at rest on the right side of the boat to the time he immediately jumped off? Where did that energy come from (provide a brief answer)?

### Diagram Explanation

The diagram on the right of the text illustrates:
- A person of mass \( m \) standing on a boat.
- The boat is depicted as a rectangle marked with its mass \( M \) and length \( L \).
- The boat's position is aligned on a horizontal \( x \)-axis, with the left side at \( x = 0 \).
- An arrow indicates the position and direction of the person and boat on the axis.
Transcribed Image Text:## Problem 2 Suppose a person of mass \( m = 75 \) kg is standing on the left end of a uniform boat of mass \( M = 200 \) kg and length \( L = 5 \) m, as shown in the sketch. The boat is on the water, which for our purposes we will consider frictionless. When the person is standing on the left end of the boat (you can consider the person to be a point particle), the left end of the boat is at \( x = 0 \) m. ### A. Where is the center of mass in \( x \) of the man-boat system? ### B. Now suppose the man walks to the right-hand edge of the boat. What is the \( x \)-coordinate of the left-hand edge of the boat? ### C. After the man arrives at the right-hand side of the boat (the man and boat are at rest), he jumps off horizontally (to the right) with speed \( v = 10 \) m/s. What is the speed of the boat? (Magnitude and direction). ### D. What is the change in kinetic energy of the man-boat system between the time he was standing at rest on the right side of the boat to the time he immediately jumped off? Where did that energy come from (provide a brief answer)? ### Diagram Explanation The diagram on the right of the text illustrates: - A person of mass \( m \) standing on a boat. - The boat is depicted as a rectangle marked with its mass \( M \) and length \( L \). - The boat's position is aligned on a horizontal \( x \)-axis, with the left side at \( x = 0 \). - An arrow indicates the position and direction of the person and boat on the axis.
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