To determine the vertical acceleration [tex]\(a_y\)[/tex] for an object in projectile motion, let's break down the components involved:
1. Understanding Projectile Motion:
- Projectile motion refers to the motion of an object that is thrown or projected into the air and is subject to only the acceleration due to gravity.
2. Vertical Acceleration [tex]\(a_y\)[/tex]:
- In the context of projectile motion, the only force acting on the object in the vertical direction (ignoring air resistance) is gravity. This leads to a constant vertical acceleration.
3. Constant Acceleration Due to Gravity:
- The acceleration due to gravity on Earth is approximately [tex]\(9.8 \, m/s^2\)[/tex].
- Since this acceleration acts downward, it is considered negative when using a coordinate system where upward is positive.
Given that the vertical acceleration [tex]\(a_y\)[/tex] for an object in projectile motion is due to gravity and acts downward, it is:
[tex]\[ a_y = -9.8 \, m/s^2 \][/tex]
Therefore, the value of [tex]\(a_y\)[/tex] for an object in projectile motion is [tex]\(-9.8 \, m/s^2\)[/tex].
So, the correct answer is:
[tex]\[ -9.8 \, m/s^2 \][/tex]
