Chekhov (mc = 60 kg), Scotty (ms = 75 kg), and Uhura (mu = 55 kg) are floating motionless in space near the Enterprise after it has been attacked by Tholians. All three are tethered with massless ropes for safety, with L₁ = 4 m, and L₂ = 2 m. They pull on their ropes to change position. At some later time, they are all again motionless, but their positions have changed as seen here. How far did Uhura move horizontally? BEFORE 4₁ 4₂ 4+2 h AFTER

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Chapter1: Units, Trigonometry. And Vectors
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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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**Scenario Description:**

Chekhov (\(m_c = 60 \, \text{kg}\)), Scotty (\(m_s = 75 \, \text{kg}\)), and Uhura (\(m_u = 55 \, \text{kg}\)) are floating motionless in space near the Enterprise after it has been attacked by Tholians. All three are tethered with massless ropes for safety, with \(L_1 = 4 \, \text{m}\) and \(L_2 = 2 \, \text{m}\). They pull on their ropes to change position. At some later time, they are all again motionless, but their positions have changed as seen in the diagram. The task is to find out how far Uhura moved horizontally.

**Diagram Explanation:**

- **Before:** 
  - Chekhov (C) is connected to Scotty (S) with a rope of length \(L_1 = 4 \, \text{m}\).
  - Uhura (U) is connected to Chekhov (C) with a rope of length \(L_2 = 2 \, \text{m}\).

- **After:**
  - The three individuals' positions have changed, but the total length of the ropes \(L_1 + L_2\) remains unchanged at 6 meters.

**Calculation:**

The problem involves calculating the horizontal movement of Uhura by considering the constraints of the rope lengths and the conserved spacings between the individuals. 

**Answer:** 
Uhura moved horizontally \(3.79 \, \text{m}\).
Transcribed Image Text:**Scenario Description:** Chekhov (\(m_c = 60 \, \text{kg}\)), Scotty (\(m_s = 75 \, \text{kg}\)), and Uhura (\(m_u = 55 \, \text{kg}\)) are floating motionless in space near the Enterprise after it has been attacked by Tholians. All three are tethered with massless ropes for safety, with \(L_1 = 4 \, \text{m}\) and \(L_2 = 2 \, \text{m}\). They pull on their ropes to change position. At some later time, they are all again motionless, but their positions have changed as seen in the diagram. The task is to find out how far Uhura moved horizontally. **Diagram Explanation:** - **Before:** - Chekhov (C) is connected to Scotty (S) with a rope of length \(L_1 = 4 \, \text{m}\). - Uhura (U) is connected to Chekhov (C) with a rope of length \(L_2 = 2 \, \text{m}\). - **After:** - The three individuals' positions have changed, but the total length of the ropes \(L_1 + L_2\) remains unchanged at 6 meters. **Calculation:** The problem involves calculating the horizontal movement of Uhura by considering the constraints of the rope lengths and the conserved spacings between the individuals. **Answer:** Uhura moved horizontally \(3.79 \, \text{m}\).
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