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Let's analyze the questions related to projectile motion:

### Part A:
**For a projectile, which of the following quantities are constant during the flight? Check all that apply.**

**Given options:**
- \( v \) (speed)
- \( a_x \) (acceleration in the x-direction)
- \( x \) (position in the x-direction)
- \( v_x \) (velocity in the x-direction)
- \( v_y \) (velocity in the y-direction)
- \( y \) (position in the y-direction)
- \( a_y \) (acceleration in the y-direction)

**Answer:**
- **\( v_x \)**: The horizontal component of velocity is constant in projectile motion (assuming no air resistance).
- **\( a_x \)**: The horizontal acceleration is zero because there is no force acting horizontally.
- **\( a_y \)**: The vertical acceleration is constant and equal to \( -g \) (the acceleration due to gravity).

Thus, the correct answers are:
- \( v_x \)
- \( a_x \)
- \( a_y \)

### Part B:
**Which of these quantities are zero throughout the flight? Check all that apply.**

**Given options:**
- \( a_y \) (acceleration in the y-direction)
- \( v_y \) (velocity in the y-direction)
- \( v \) (speed)
- \( a_x \) (acceleration in the x-direction)
- \( y \) (position in the y-direction)
- \( x \) (position in the x-direction)
- \( v_x \) (velocity in the x-direction)

**Answer:**
- **\( a_x \)**: The horizontal acceleration is zero throughout the flight (no horizontal force acting).

Thus, the correct answer is:
- \( a_x \)

Do you want details or have any questions?

Here are 5 related questions that expand on this information:
1. How does air resistance affect the constancy of \( v_x \) and \( a_x \) in projectile motion?
2. What are the equations of motion for a projectile in both the x and y directions?
3. How can you determine the maximum height reached by a projectile?
4. What is the significance of the angle of projection in determining the range of a projectile?
5. How does the initial velocity affect the trajectory of a projectile?

**Tip:** In projectile motion, understanding the independence of horizontal and vertical components of motion helps in solving complex problems more easily.

For a projectile, which of the following quantities are constant during the flight? Which of these quantities are zero throughout the flight?

Understand which quantities are constant and which are zero during the flight of a projectile. This problem explores concepts in projectile motion and kinematics, suitable for students in Grades 10-12.

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