Men’s Pole Vault
yi = + 3.5 m yf = ___________________ 𝒔𝒚 = ___________________
d = _____________
v avg = __________________ 𝒗𝒂𝒗𝒈 = ___________________________
Men’s 50 m Freestyle Swim
xi = 0 m xf = ___________________ 𝒔𝒙 = ___________________
d = _____________
v avg = __________________ 𝒗𝒂𝒗𝒈 = ___________________________

Calculate the initial position, yi, final position, yf , displacement, 𝒔𝒚 , distance, d and average speed, vavg and
average velocity, vavg for the pole vault from when he releases his pole? He sets a new Olympic record of 6.2
m. (Assume he starts 3.5 meters up when he releases the pole from the ground and until he reaches the
cushions below which are 1 meter above the ground. The whole trip after he releases the pole to when he hits
the cushion takes ~1.77 seconds.
Release is 3.5 m
above the ground

cushion is 1 meter off the ground

To solve this problem, we'll analyze the pole vault scenario and calculate the values requested, assuming the athlete sets a new Olympic record of 6.2 meters. We'll follow the steps below:

### Men’s Pole Vault

1. **Initial Position, \( y_i \)**:
   - Given: \( y_i = 3.5 \) meters (The height from which the vaulter releases the pole)

2. **Final Position, \( y_f \)**:
   - The final position is the height of the cushion where the vaulter lands.
   - Given: \( y_f = 1.0 \) meter (Height of the cushion above the ground)

3. **Vertical Displacement, \( s_y \)**:
   - Displacement is calculated as the difference between the final and initial positions.
   \[
   s_y = y_f - y_i = 1.0 \, \text{m} - 3.5 \, \text{m} = -2.5 \, \text{m}
   \]
   - The negative sign indicates the vaulter moved downward.

4. **Distance, \( d \)**:
   - The distance traveled is the magnitude of the vertical displacement.
   \[
   d = |s_y| = 2.5 \, \text{m}
   \]

5. **Average Speed, \( v_{\text{avg}} \)**:
   - Average speed is the total distance divided by the total time.
   \[
   v_{\text{avg}} = \frac{d}{t} = \frac{2.5 \, \text{m}}{1.77 \, \text{s}} \approx 1.41 \, \text{m/s}
   \]

6. **Average Velocity, \( \bar{v} \)**:
   - Average velocity is the displacement divided by the total time.
   \[
   \bar{v} = \frac{s_y}{t} = \frac{-2.5 \, \text{m}}{1.77 \, \text{s}} \approx -1.41 \, \text{m/s}
   \]
   - The negative sign indicates the direction of the motion (downward).

### Summary:
- **\( y_i = 3.5 \, \text{m} \)**
- **\( y_f = 1.0 \, \text{m} \)**
- **\( s_y = -2.5 \, \text{m} \)**
- **\( d = 2.5 \, \text{m} \)**
- **\( v_{\text{avg}} = 1.41 \, \text{m/s} \)**
- **\( \bar{v} = -1.41 \, \text{m/s} \)**

Would you like to go over any specific calculation or need additional details?

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### Related Questions:
1. How would the average velocity change if the cushion height was higher?
2. What would be the impact on average speed if the time taken was shorter?
3. How does the vaulter's initial speed affect the outcome of the vault?
4. What role does gravity play in determining the final velocity before hitting the cushion?
5. How would air resistance affect the vaulter's speed and time of flight?

### Tip:
When solving problems involving displacement, always pay attention to the signs; they indicate the direction of the movement, which is crucial for interpreting velocity correctly.

Learn how to calculate the initial position, displacement, distance, average speed, and average velocity for a men’s pole vault scenario where an athlete sets a new Olympic record. Includes step-by-step calculations and explanations.

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