https://r2.erweima.ai/mathbot/image/17253813201389y1m6r8g.jpg

Selecciona dos de los siguientes deportes y utilizando la velocidad de pelota y la fórmula que
está a continuación, calcula los grados con los que fue lanzada la pelota si se mantiene 3
segundos en el aire.

To solve this problem, we need to:

1. Choose two sports from the provided image.
2. Use the ball speed given for each sport.
3. Apply the given formula, which seems to involve calculating the angle at which the ball was thrown if it stayed in the air for 3 seconds.

### Image Content Analysis
From the image, we can identify the following sports and their corresponding ball speeds:

1. **Tennis**: 263.4 km/h
2. **Golf**: 349.5 km/h
3. **Baseball**: 174.0 km/h
4. **Squash**: 281.6 km/h
5. **Football (Soccer)**: 131.8 km/h
6. **Jai Alai**: 302.0 km/h
7. **Badminton**: 493.0 km/h

### Formula Application
Since the image mentioned a formula, I'll assume it's the standard projectile motion equation for the range, time of flight, or angle of projection. For a projectile that stays in the air for \( T \) seconds:

\[ T = \frac{2v_0 \sin(\theta)}{g} \]

Where:
- \( T \) is the time the ball stays in the air (3 seconds in this case).
- \( v_0 \) is the initial speed (in m/s).
- \( \theta \) is the angle of projection.
- \( g \) is the acceleration due to gravity (\( 9.8 \, \text{m/s}^2 \)).

We can rearrange the formula to solve for \( \theta \):

\[ \theta = \arcsin\left(\frac{gT}{2v_0}\right) \]

### Converting Speeds
Since the speeds are given in km/h, we need to convert them to m/s:

\[ v_0 (\text{in m/s}) = \frac{\text{speed in km/h} \times 1000}{3600} \]

### Let's Calculate the Angles

I'll perform the calculations for two selected sports: **Golf** and **Baseball**.

1. **Golf:**
   - Speed: 349.5 km/h = \( \frac{349.5 \times 1000}{3600} \) m/s

2. **Baseball:**
   - Speed: 174.0 km/h = \( \frac{174.0 \times 1000}{3600} \) m/s

Let me compute these angles for you.The calculated angles for the two selected sports are as follows:

1. **Golf**: The ball was launched at an angle of approximately **8.71°**.
2. **Baseball**: The ball was launched at an angle of approximately **17.71°**.

These angles ensure that the ball remains in the air for 3 seconds under the given conditions.

Would you like more details or have any further questions?

### Related Questions:
1. How does changing the initial speed affect the angle for the same time of flight?
2. What is the significance of the angle in determining the maximum height reached by the projectile?
3. How would the angles change if the ball stays in the air for a different duration?
4. What would happen to the angle if the speed were doubled?
5. How does air resistance affect the calculated angles in real-world scenarios?

### Tip:
When working with projectile motion, always ensure that all units are consistent, especially when converting speeds.

Learn how to calculate the launch angles of balls in various sports using projectile motion equations. This problem involves determining the angles at which balls are thrown to remain in the air for 3 seconds based on their given speeds. Suitable for high school students studying physics and trigonometry.

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