Answer :
When understanding the motion of projectiles under the influence of gravity, there are a couple of fundamental principles in physics we need to consider.
1. Horizontal Motion: The horizontal velocity of a projectile remains constant if we neglect air resistance. This is because there are no horizontal forces acting on the projectile (neglecting air resistance), which implies no horizontal acceleration. Therefore, the horizontal velocity of projectile [tex]\( X \)[/tex] will be constant.
2. Vertical Motion: The vertical component of a projectile's velocity changes due to the acceleration caused by gravity. Specifically, the acceleration due to gravity is approximately [tex]\( 9.8 \, \text{m/s}^2 \)[/tex] downward. This means the vertical velocity of projectile [tex]\( Y \)[/tex] will change over time.
Given these principles, let's analyze the options provided:
- Option 1: "The horizontal velocity of projectile [tex]\( X \)[/tex] is changing, and the vertical velocity of projectile [tex]\( Y \)[/tex] is constant."
- This is incorrect because the horizontal velocity should remain constant and the vertical velocity should change due to gravity.
- Option 2: "The vertical velocity of projectile [tex]\( Y \)[/tex] is changing, and the horizontal velocity of projectile [tex]\( X \)[/tex] is constant."
- This is correct. The vertical velocity of [tex]\( Y \)[/tex] changes due to the gravitational pull, and the horizontal velocity of [tex]\( X \)[/tex] remains constant.
- Option 3: "The horizontal acceleration of projectile [tex]\( X \)[/tex] is [tex]\( -9.8 \, \text{m/s}^2 \)[/tex], and the vertical acceleration of projectile [tex]\( Y \)[/tex] is [tex]\( 0 \, \text{m/s}^2 \)[/tex]."
- This is incorrect because the horizontal acceleration should be [tex]\( 0 \, \text{m/s}^2 \)[/tex] (no horizontal force), and the vertical acceleration should be [tex]\( -9.8 \, \text{m/s}^2 \)[/tex] due to gravity.
- Option 4: "The horizontal acceleration of projectile [tex]\( Y \)[/tex] is [tex]\( -9.8 \, \text{m/s}^2 \)[/tex], and the vertical acceleration of projectile [tex]\( Y \)[/tex] is [tex]\( 0 \, \text{m/s}^2 \)[/tex]."
- This is also incorrect for the same reasons as Option 3; the vertical acceleration should be [tex]\( -9.8 \, \text{m/s}^2 \)[/tex], not the horizontal acceleration.
Therefore, the best description of the motion of the projectiles is:
- The vertical velocity of projectile [tex]\( Y \)[/tex] is changing, and the horizontal velocity of projectile [tex]\( X \)[/tex] is constant.
So, the correct answer is:
The vertical velocity of projectile [tex]\( Y \)[/tex] is changing, and the horizontal velocity of projectile [tex]\( X \)[/tex] is constant.
1. Horizontal Motion: The horizontal velocity of a projectile remains constant if we neglect air resistance. This is because there are no horizontal forces acting on the projectile (neglecting air resistance), which implies no horizontal acceleration. Therefore, the horizontal velocity of projectile [tex]\( X \)[/tex] will be constant.
2. Vertical Motion: The vertical component of a projectile's velocity changes due to the acceleration caused by gravity. Specifically, the acceleration due to gravity is approximately [tex]\( 9.8 \, \text{m/s}^2 \)[/tex] downward. This means the vertical velocity of projectile [tex]\( Y \)[/tex] will change over time.
Given these principles, let's analyze the options provided:
- Option 1: "The horizontal velocity of projectile [tex]\( X \)[/tex] is changing, and the vertical velocity of projectile [tex]\( Y \)[/tex] is constant."
- This is incorrect because the horizontal velocity should remain constant and the vertical velocity should change due to gravity.
- Option 2: "The vertical velocity of projectile [tex]\( Y \)[/tex] is changing, and the horizontal velocity of projectile [tex]\( X \)[/tex] is constant."
- This is correct. The vertical velocity of [tex]\( Y \)[/tex] changes due to the gravitational pull, and the horizontal velocity of [tex]\( X \)[/tex] remains constant.
- Option 3: "The horizontal acceleration of projectile [tex]\( X \)[/tex] is [tex]\( -9.8 \, \text{m/s}^2 \)[/tex], and the vertical acceleration of projectile [tex]\( Y \)[/tex] is [tex]\( 0 \, \text{m/s}^2 \)[/tex]."
- This is incorrect because the horizontal acceleration should be [tex]\( 0 \, \text{m/s}^2 \)[/tex] (no horizontal force), and the vertical acceleration should be [tex]\( -9.8 \, \text{m/s}^2 \)[/tex] due to gravity.
- Option 4: "The horizontal acceleration of projectile [tex]\( Y \)[/tex] is [tex]\( -9.8 \, \text{m/s}^2 \)[/tex], and the vertical acceleration of projectile [tex]\( Y \)[/tex] is [tex]\( 0 \, \text{m/s}^2 \)[/tex]."
- This is also incorrect for the same reasons as Option 3; the vertical acceleration should be [tex]\( -9.8 \, \text{m/s}^2 \)[/tex], not the horizontal acceleration.
Therefore, the best description of the motion of the projectiles is:
- The vertical velocity of projectile [tex]\( Y \)[/tex] is changing, and the horizontal velocity of projectile [tex]\( X \)[/tex] is constant.
So, the correct answer is:
The vertical velocity of projectile [tex]\( Y \)[/tex] is changing, and the horizontal velocity of projectile [tex]\( X \)[/tex] is constant.