Final answer:
The y-component of the acceleration of an object in projectile motion is -9.8 m/s², reflecting the constant acceleration due to gravity. This assumes the standard convention of upwards as the positive y-axis direction.
Step-by-step explanation:
When analyzing the motion of projectiles, it's essential to consider both velocity and acceleration components along the x- (horizontal) and y- (vertical) axes. Given that other forces such as air resistance are negligible, the y-component of the acceleration of a projectile is a very specific value, determined by the acceleration due to gravity.
In the conventional axis system where upwards is positive, the acceleration due to gravity acts in the negative y-direction. Thus, the y-component of a projectile's acceleration is -9.8 m/s², which aligns with the standard acceleration due to gravity at Earth's surface, designated by the symbol g. This acceleration remains constant throughout the projectile's motion. Therefore, the correct answer to the student's question is option b: The y-component of the acceleration of an object experiencing projectile motion is equal to the acceleration due to gravity, and since the conventional choice of axis assumes upward as positive, the acceleration due to gravity is negative, i.e., -9.8 m/s².
The x-component of the acceleration remains 0 throughout the projectile's trajectory, as gravity acts solely in the vertical direction and no horizontal forces are acting on the projectile when air resistance is ignored.