A girl of mass m. is standing on a plank of mass mp. Both are originally at rest on a frozen lake that constitutes a frictionless, flat surface The girl begins to walk along the plank at a constant velocity v gp to the right relative to the plank. (The subscript GP denotes the girl relative to the plank.) (a) What is the velocity vpr of the plank relative to the surface of the ice? (Use the following as necessary: vep, me, and mp. Indicate the direction with the sign of your answer. Let the positive direction be in the direction that the girl walks.) PI (b) What is the girl's velocity var relative to the ice surface? (Use the following as necessary: VGp, mg and mp. Indicate the direction with the sign of your answer. Let the positive direction be in the direction that the girl walks.) GI

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### Physics Problem on Relative Motion

**Scenario:**
A girl of mass \( m_G \) is standing on a plank of mass \( m_P \). Both are originally at rest on a frozen lake that constitutes a frictionless, flat surface. The girl begins to walk along the plank at a constant velocity \( \vec{v}_{GP} \) to the right relative to the plank. (The subscript GP denotes the girl relative to the plank.)

#### Problem:
(a) What is the velocity \( \vec{v}_{PI} \) of the plank relative to the surface of the ice? (Use the following as necessary: \( \vec{v}_{GP} \), \( m_G \), and \( m_P \). Indicate the direction with the sign of your answer. Let the positive direction be in the direction that the girl walks.)

\[ \vec{v}_{PI} = \boxed{\phantom{\text{Answer here}}} \]

(b) What is the girl's velocity \( \vec{v}_{GI} \) relative to the ice surface? (Use the following as necessary: \( \vec{v}_{GP} \), \( m_G \), and \( m_P \). Indicate the direction with the sign of your answer. Let the positive direction be in the direction that the girl walks.)

\[ \vec{v}_{GI} = \boxed{\phantom{\text{Answer here}}} \]

#### Detailed Explanation:
1. **Understanding the Situation:**
   - **Masses:**
     - \( m_G \): Mass of the girl.
     - \( m_P \): Mass of the plank.
   - **Relative Velocity \( \vec{v}_{GP} \):** The velocity of the girl walking on the plank relative to the plank.

2. **Frictionless Surface Impact:**
   - Since the ice surface is frictionless, the total momentum of the system (girl + plank) must stay constant.
   - Initially, both the girl and plank are at rest, so the total initial momentum is zero.

3. **Conservation of Momentum:**
   - When the girl starts walking to the right (positive direction), the plank will move to the left (negative direction) to conserve momentum.
   - Let's denote:
     - \( \vec{v}_{PI} \): Velocity of the plank relative to the ice.
     - \( \vec{v}_{GI} \
Transcribed Image Text:### Physics Problem on Relative Motion **Scenario:** A girl of mass \( m_G \) is standing on a plank of mass \( m_P \). Both are originally at rest on a frozen lake that constitutes a frictionless, flat surface. The girl begins to walk along the plank at a constant velocity \( \vec{v}_{GP} \) to the right relative to the plank. (The subscript GP denotes the girl relative to the plank.) #### Problem: (a) What is the velocity \( \vec{v}_{PI} \) of the plank relative to the surface of the ice? (Use the following as necessary: \( \vec{v}_{GP} \), \( m_G \), and \( m_P \). Indicate the direction with the sign of your answer. Let the positive direction be in the direction that the girl walks.) \[ \vec{v}_{PI} = \boxed{\phantom{\text{Answer here}}} \] (b) What is the girl's velocity \( \vec{v}_{GI} \) relative to the ice surface? (Use the following as necessary: \( \vec{v}_{GP} \), \( m_G \), and \( m_P \). Indicate the direction with the sign of your answer. Let the positive direction be in the direction that the girl walks.) \[ \vec{v}_{GI} = \boxed{\phantom{\text{Answer here}}} \] #### Detailed Explanation: 1. **Understanding the Situation:** - **Masses:** - \( m_G \): Mass of the girl. - \( m_P \): Mass of the plank. - **Relative Velocity \( \vec{v}_{GP} \):** The velocity of the girl walking on the plank relative to the plank. 2. **Frictionless Surface Impact:** - Since the ice surface is frictionless, the total momentum of the system (girl + plank) must stay constant. - Initially, both the girl and plank are at rest, so the total initial momentum is zero. 3. **Conservation of Momentum:** - When the girl starts walking to the right (positive direction), the plank will move to the left (negative direction) to conserve momentum. - Let's denote: - \( \vec{v}_{PI} \): Velocity of the plank relative to the ice. - \( \vec{v}_{GI} \
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