In the figure below, a frictionless roller coaster crosses the first hill of height h = 55.5 m with %3D an initial speed of v; = 15.0 m/s. First hill h/2 a) What is the speed of the coaster at point A? b) How high will the coaster go on the last hill (beyond point B), which is too high for it to cross?

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Chapter1: Units, Trigonometry. And Vectors
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**Title: Understanding Roller Coaster Dynamics**

In the figure below, a frictionless roller coaster crosses the first hill of height \( h = 55.5 \, \text{m} \) with an initial speed of \( v_i = 15.0 \, \text{m/s} \).

The diagram illustrates a roller coaster track. The track has a series of hills and dips:

1. **First Hill**: The roller coaster begins at the top of a hill with height \( h \).
2. The track then descends and ascends to another hill of the same height \( h \).
3. **Point A**: Midway between this hill and the next dip, where the height is \( h/2 \).
4. **Point B**: Lowest point in a dip beyond point A.

**Questions:**

a) What is the speed of the coaster at point A?

b) How high will the coaster go on the last hill (beyond point B), which is too high for it to cross?

**Explanation:**
- The track is pink and follows a sinusoidal path. 
- The background shows a grid indicating measurement units for height. 

Understanding energy conservation and speed changes at different points will help answer the questions.
Transcribed Image Text:**Title: Understanding Roller Coaster Dynamics** In the figure below, a frictionless roller coaster crosses the first hill of height \( h = 55.5 \, \text{m} \) with an initial speed of \( v_i = 15.0 \, \text{m/s} \). The diagram illustrates a roller coaster track. The track has a series of hills and dips: 1. **First Hill**: The roller coaster begins at the top of a hill with height \( h \). 2. The track then descends and ascends to another hill of the same height \( h \). 3. **Point A**: Midway between this hill and the next dip, where the height is \( h/2 \). 4. **Point B**: Lowest point in a dip beyond point A. **Questions:** a) What is the speed of the coaster at point A? b) How high will the coaster go on the last hill (beyond point B), which is too high for it to cross? **Explanation:** - The track is pink and follows a sinusoidal path. - The background shows a grid indicating measurement units for height. Understanding energy conservation and speed changes at different points will help answer the questions.
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