Is there any point along the path of a projectile where its velocity and acceleration vectors are;

a) perpendicular to each other
b) parallel to each other?

My ans:
a) I thought its perpendicular at the peak but I didn't know how to explain it
b) I thought they would be parallel when the ball is either going up or down

a) is correct. Gravity is downward, velocity it parallel to Earth.

b) correct.

To determine the points along the path of a projectile where its velocity and acceleration vectors are perpendicular or parallel to each other, we need to consider the nature of projectile motion.

Projectile motion occurs when an object is launched into the air and follows a curved path under the influence of gravity. The motion is characterized by both a horizontal component (velocity) and a vertical component (acceleration due to gravity).

a) Perpendicular vectors: The velocity and acceleration vectors of a projectile can be perpendicular to each other at two specific points along the path:

1. At the highest point of the projectile's motion: When a projectile reaches its peak height, its velocity vector becomes zero while gravity continues to pull it downward. At this instantaneous moment, the acceleration vector is completely downward due to gravity, and therefore perpendicular to the zero velocity vector.

2. At the lowest point of the projectile's motion: Similarly, when a projectile reaches its lowest point in the trajectory, its velocity vector once again becomes zero. At this moment, the acceleration vector is again perpendicular to the zero velocity vector. However, it is important to note that this instance occurs only if the projectile is launched vertically and reaches its original launch height.

b) Parallel vectors: There are no points along the path of a purely projectile motion where the velocity and acceleration vectors are parallel to each other.

It is crucial to understand that while the velocity and acceleration vectors are not parallel, they are related. The acceleration vector constantly changes the velocity vector's direction while its magnitude remains constant (due to the influence of gravity). This leads to the curved trajectory typically associated with projectile motion.