The Xanthar mothership locks onto an enemy cruiser with its tractor beam (see the figure below); each ship is at rest in deep space with no propulsion following a devastating battle. The mothership is at x = 0 when its tractor beams are first engaged, a distance d = 205 xiles from the cruiser. Determine the x-position in xiles (measured from x = 0) of the two spacecraft when the tractor beam has pulled them together. Model each spacecraft as a point particle with the mothership of mass M = 175 xons and the cruiser of mass m = 10.0 xons. HINT xiles Need Help? x=0) Read It M Watch It m ===== Ⓡ

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### Tractor Beam Mechanics in Space

#### Scenario:
The Xanthar mothership locks onto an enemy cruiser with its tractor beam. Both spacecrafts are initially at rest in deep space without propulsion following a battle.

#### Variables and Initial Conditions:
- **Mothership Position:** \( x = 0 \)
- **Distance Between Ships:** \( d = 205 \) xiles
- **Mothership Mass:** \( M = 175 \) xons
- **Cruiser Mass:** \( m = 10.0 \) xons

#### Objective:
Determine the x-position in xiles (measured from \( x = 0 \)) of both spacecrafts when the tractor beam pulls them together.

#### Diagram Description:
- The left side of the diagram represents the Xanthar mothership, labeled as \( M \).
- A yellow beam represents the activated tractor beam pulling the cruiser towards the mothership.
- The separation distance \( d \) is marked along the x-axis from \( x = 0 \) to the cruiser.
- The variable \( x \) is denoted for position measurements along the x-axis.

**Note:** Each spacecraft is modeled as a point particle for simplification.

#### Problem Statement:
By using the given information and assuming that \( d = 205 \) xiles, \( M = 175 \) xons, and \( m = 10.0 \) xons, calculate the respective x-positions of the mothership and the cruiser when they meet.

**Input Box:** 
An input field is provided for entering the final x-position in xiles.

**Help Section:**
Buttons labeled "Read It" and "Watch It" are available for additional instructions and visual guidance.

#### Additional Information:
Understanding momentum conservation principles and center of mass calculations will be critical in solving this problem.

### Need Help?
- **Read It:** Access detailed written explanations.
- **Watch It:** View visual demonstrations and video tutorials.
Transcribed Image Text:### Tractor Beam Mechanics in Space #### Scenario: The Xanthar mothership locks onto an enemy cruiser with its tractor beam. Both spacecrafts are initially at rest in deep space without propulsion following a battle. #### Variables and Initial Conditions: - **Mothership Position:** \( x = 0 \) - **Distance Between Ships:** \( d = 205 \) xiles - **Mothership Mass:** \( M = 175 \) xons - **Cruiser Mass:** \( m = 10.0 \) xons #### Objective: Determine the x-position in xiles (measured from \( x = 0 \)) of both spacecrafts when the tractor beam pulls them together. #### Diagram Description: - The left side of the diagram represents the Xanthar mothership, labeled as \( M \). - A yellow beam represents the activated tractor beam pulling the cruiser towards the mothership. - The separation distance \( d \) is marked along the x-axis from \( x = 0 \) to the cruiser. - The variable \( x \) is denoted for position measurements along the x-axis. **Note:** Each spacecraft is modeled as a point particle for simplification. #### Problem Statement: By using the given information and assuming that \( d = 205 \) xiles, \( M = 175 \) xons, and \( m = 10.0 \) xons, calculate the respective x-positions of the mothership and the cruiser when they meet. **Input Box:** An input field is provided for entering the final x-position in xiles. **Help Section:** Buttons labeled "Read It" and "Watch It" are available for additional instructions and visual guidance. #### Additional Information: Understanding momentum conservation principles and center of mass calculations will be critical in solving this problem. ### Need Help? - **Read It:** Access detailed written explanations. - **Watch It:** View visual demonstrations and video tutorials.
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