Calculate the final velocity right after a 18 kg rugby player who is initially running at 7.15 m/s collides head-on with a padded goalpost and experiences a backward force of 17500 N for 5.50 x 10-2 s. Question Credit: OpenStax College Physics final velocity: m/s

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**Problem Statement:**

Calculate the final velocity right after a 118 kg rugby player who is initially running at 7.15 m/s collides head-on with a padded goalpost and experiences a backward force of 17500 N for 5.50 × 10⁻² s.

**Solution:**

[final velocity: ________ m/s]

**Question Credit:** OpenStax College Physics

**Explanation:**

To solve this problem, we will use the principle of impulse and momentum. The impulse experienced by the player is equal to the change in momentum. The impulse can be calculated as the product of the force and the time duration it is applied, and the change in momentum is the difference between the final and initial momentum.

**Step-by-step solution:**

1. **Identify the given values:**
   - Mass of the player (m) = 118 kg
   - Initial velocity (u) = 7.15 m/s
   - Force (F) = 17500 N (acting backward)
   - Time duration (t) = 5.50 × 10⁻² s

2. **Calculate the impulse (I):**
   - Impulse, \( I = F \times t \)
   - \( I = 17500 \, \text{N} \times 5.50 \times 10^{-2} \, \text{s} \)

3. **Calculate the initial momentum (p_initial):**
   - \( p_{\text{initial}} = m \times u \)
   - \( p_{\text{initial}} = 118 \, \text{kg} \times 7.15 \, \text{m/s} \)

4. **Use impulse-momentum theorem:**
   - \( I = p_{\text{final}} - p_{\text{initial}} \)
   - Rearrange to find final momentum: \( p_{\text{final}} = I + p_{\text{initial}} \)

5. **Find final velocity (v):**
   - \( v = \frac{p_{\text{final}}}{m} \)

By performing these calculations, you will find the final velocity of the rugby player after the collision.
Transcribed Image Text:**Problem Statement:** Calculate the final velocity right after a 118 kg rugby player who is initially running at 7.15 m/s collides head-on with a padded goalpost and experiences a backward force of 17500 N for 5.50 × 10⁻² s. **Solution:** [final velocity: ________ m/s] **Question Credit:** OpenStax College Physics **Explanation:** To solve this problem, we will use the principle of impulse and momentum. The impulse experienced by the player is equal to the change in momentum. The impulse can be calculated as the product of the force and the time duration it is applied, and the change in momentum is the difference between the final and initial momentum. **Step-by-step solution:** 1. **Identify the given values:** - Mass of the player (m) = 118 kg - Initial velocity (u) = 7.15 m/s - Force (F) = 17500 N (acting backward) - Time duration (t) = 5.50 × 10⁻² s 2. **Calculate the impulse (I):** - Impulse, \( I = F \times t \) - \( I = 17500 \, \text{N} \times 5.50 \times 10^{-2} \, \text{s} \) 3. **Calculate the initial momentum (p_initial):** - \( p_{\text{initial}} = m \times u \) - \( p_{\text{initial}} = 118 \, \text{kg} \times 7.15 \, \text{m/s} \) 4. **Use impulse-momentum theorem:** - \( I = p_{\text{final}} - p_{\text{initial}} \) - Rearrange to find final momentum: \( p_{\text{final}} = I + p_{\text{initial}} \) 5. **Find final velocity (v):** - \( v = \frac{p_{\text{final}}}{m} \) By performing these calculations, you will find the final velocity of the rugby player after the collision.
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