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Let's analyze this problem step-by-step.

### **Problem Overview:**
1. A train moves **eastward** at constant speed \(v_T\).
2. A cyclist travels at a speed \(v_C\) at **15° east of north** with respect to the ground.
3. **Condition:** \(v_C < v_T\), meaning the cyclist is slower than the train.
4. The problem asks: Which vector options correctly represent the cyclist’s velocity **as seen from Car 1** and **as seen from Car 3**? Both cars are on the train, moving east at speed \(v_T\).

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### **Key Concept: Relative Velocity:**
When measuring velocity from a moving frame of reference (like a car on the train), we need to subtract the velocity of the reference frame (train) from the velocity of the cyclist in the ground frame.

- **Velocity of the cyclist w.r.t. Car 1 and Car 3:**  
  \( \vec{v}_{C,\text{relative}} = \vec{v}_C - \vec{v}_T \)  
  (Since both Car 1 and Car 3 are on the train, the relative velocity in both cases involves subtracting the same train velocity.)

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### **Cyclist's Ground Velocity:**
- The cyclist’s velocity, \( \vec{v}_C \), is **15° east of north**.
  - This means it has a **northward component** and a **small eastward component**.

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### **Relative Velocity Directions (Key Insight):**
- The train moves eastward, so when subtracting the train's eastward velocity from the cyclist’s velocity:
  - **Eastward components:** The eastward velocity of the train is much larger than that of the cyclist, so the eastward component in the relative velocity will point **westward**.
  - **Northward component:** The northward component of the cyclist remains unaffected since the train only moves east.

Thus:
- **Relative velocity of cyclist from both cars** will point slightly **northwest** (since the eastward component becomes negative, and the northward component remains positive).

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### **Correct Option:**
- Both Car 1 and Car 3 should measure the velocity of the cyclist as pointing **northwest**.

This matches **Option C**:  
Both vectors point northwest, which is consistent with the reasoning above.

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### **Answer:**
**Option C** is correct.

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Would you like a breakdown of the relative velocity calculations or any further clarifications?

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### **Related Questions:**
1. How do we break a vector into components?
2. What would change if \(v_C > v_T\)?
3. How does relative velocity affect perception in non-inertial frames?
4. What would the velocity look like from a stationary observer on the ground?
5. How does vector subtraction work in general physics problems?

**Tip:** When dealing with relative motion, always visualize component-wise subtraction for clarity.

A train is traveling east at a constant speed. A cyclist is moving at a constant speed less than the train's speed, at an angle of 15° east of north with respect to the ground. Which of the following vectors represents the velocity of the cyclist as seen from observers in Car 1 and Car 3 on the train?

Understand how to calculate the relative velocity of a cyclist moving at 15° east of north with respect to a train traveling eastward at a constant speed. Learn about vector subtraction and relative motion concepts. Suitable for students in Grades 11-12 studying physics.

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