(XC) Sally Science hits a golf shot that travels at 31.88 m/s. The shot strikes a tree and bounces back to the tee at 7.97 m/s (exactly one-fourth the initial speed). The round trip from tee to tree to tee again took exactly 3.82 seconds. How far away is the tree from the tee?

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Chapter1: Units, Trigonometry. And Vectors
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13. Please answer this ASAP. It's pyshics. 

**Problem 13:**

Sally Science hits a golf shot that travels at 31.88 m/s. The shot strikes a tree and bounces back to the tee at 7.97 m/s (exactly one-fourth the initial speed). The round trip from tee to tree to tee again took exactly 3.82 seconds. How far away is the tree from the tee?

---

### Explanation:

In this problem, we need to calculate the distance the golf ball travels to the tree and back, given its speeds and total travel time. Here is a breakdown of the approach:

1. **Initial Speed to the Tree**: 31.88 m/s
2. **Speed Back to the Tee**: 7.97 m/s (one-fourth of the initial speed)
3. **Total Round Trip Time**: 3.82 seconds

Let's denote the distance to the tree as \( d \).

- **Time to the Tree**: \( \frac{d}{31.88} \)
- **Time Back to the Tee**: \( \frac{d}{7.97} \)

The sum of these times is the total round trip time:

\[
\frac{d}{31.88} + \frac{d}{7.97} = 3.82
\]

Solving this equation will give us the distance \( d \).
Transcribed Image Text:**Problem 13:** Sally Science hits a golf shot that travels at 31.88 m/s. The shot strikes a tree and bounces back to the tee at 7.97 m/s (exactly one-fourth the initial speed). The round trip from tee to tree to tee again took exactly 3.82 seconds. How far away is the tree from the tee? --- ### Explanation: In this problem, we need to calculate the distance the golf ball travels to the tree and back, given its speeds and total travel time. Here is a breakdown of the approach: 1. **Initial Speed to the Tree**: 31.88 m/s 2. **Speed Back to the Tee**: 7.97 m/s (one-fourth of the initial speed) 3. **Total Round Trip Time**: 3.82 seconds Let's denote the distance to the tree as \( d \). - **Time to the Tree**: \( \frac{d}{31.88} \) - **Time Back to the Tee**: \( \frac{d}{7.97} \) The sum of these times is the total round trip time: \[ \frac{d}{31.88} + \frac{d}{7.97} = 3.82 \] Solving this equation will give us the distance \( d \).
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