In the context of projectile motion, the velocity and acceleration vectors behave in distinct ways throughout the trajectory of the projectile.
a) Perpendicular: Yes, there is a point during the motion where the velocity and acceleration vectors are perpendicular to each other. This occurs at the peak of the projectile’s path. At this point, the vertical component of the velocity is zero, but the acceleration due to gravity is acting downward. Therefore, the acceleration vector points downward while the instantaneous velocity vector momentarily has no vertical component and only horizontal motion, making them perpendicular.
b) Parallel: No, the velocity and acceleration vectors are never parallel in the context of ideal projectile motion. The acceleration due to gravity always acts downward, while the velocity vector changes direction as the projectile moves along its curved path. The only instance when they might seem to align is when the projectile is in free fall after reaching its peak, but even then, they are not parallel as the velocity continues in the direction of motion while the acceleration is always directed downwards.
In summary, the velocity and acceleration vectors are perpendicular at the peak of the trajectory, but they are never parallel at any point during projectile motion.