2. A boy throws a ball horizontally from the top of a building. The initial speed of the ball is 31m/s. Find the horizontal and vertical velocity of the ball after 22s.

To solve this problem, we need to analyze the horizontal and vertical components of the velocity of the ball separately.

### Given:
- Initial horizontal speed \( v_{x0} = 31 \, \text{m/s} \)
- Time \( t = 22 \, \text{s} \)
- Acceleration due to gravity \( g = 9.8 \, \text{m/s}^2 \)
- Initial vertical speed \( v_{y0} = 0 \, \text{m/s} \) (since the ball is thrown horizontally)

### Horizontal Velocity:
The horizontal velocity remains constant because there is no horizontal acceleration (assuming no air resistance).
\[
v_x = v_{x0} = 31 \, \text{m/s}
\]

### Vertical Velocity:
The vertical velocity is affected by gravity. The vertical velocity after time \( t \) is given by:
\[
v_y = v_{y0} + g \times t
\]
Since \( v_{y0} = 0 \, \text{m/s} \), we have:
\[
v_y = 0 + (9.8 \, \text{m/s}^2) \times 22 \, \text{s}
\]
\[
v_y = 215.6 \, \text{m/s}
\]

### Final Answer:
- **Horizontal velocity after 22 seconds**: \( v_x = 31 \, \text{m/s} \)
- **Vertical velocity after 22 seconds**: \( v_y = 215.6 \, \text{m/s} \)

Would you like any further details or explanations? Here are 5 related questions:

1. How do you calculate the time of flight for a projectile launched horizontally?
2. What is the formula to calculate the range of a projectile?
3. How does air resistance affect the motion of a projectile?
4. Can you explain the concept of relative velocity in projectile motion?
5. What is the significance of the angle of projection in projectile motion?

**Tip:** In projectile motion, always break the motion into horizontal and vertical components to simplify the analysis.

Explore how to calculate the horizontal and vertical velocities of a ball thrown horizontally from a building. Understand the key formulas for projectile motion, including velocity components and the effect of gravity. Suitable for advanced high school students.

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