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?
a) Yes, there is a point along the path of a projectile where its velocity and acceleration vectors are perpendicular to each other. This occurs at the highest point of the projectile's trajectory, when it reaches its maximum height. At this point, the projectile momentarily comes to a stop before reversing its motion. The velocity vector is pointing vertically upward, while the acceleration due to gravity is pointing vertically downward. Since the two vectors are in opposite directions and have no components in the same direction, they are perpendicular to each other.
b) No, there is no point along the path of a projectile where its velocity and acceleration vectors are parallel to each other. The acceleration due to gravity is constant and always points vertically downward. However, the velocity vector of the projectile changes direction continuously due to gravity. As a result, the velocity and acceleration vectors are always at an angle to each other, never parallel.