Final answer:
In projectile motion, the velocity (v) and acceleration (a) vectors are perpendicular at the apex of the trajectory where the vertical component of velocity is zero, and the velocity vector is horizontal while the acceleration due to gravity is vertical.
Step-by-step explanation:
The question asks if there is any point on the trajectory where the velocity (v) and acceleration (a) vectors are perpendicular to each other in the context of projectile motion. In projectile motion, the only force acting on the object is gravity, which means the acceleration due to gravity is constant and acts vertically downward throughout the motion. The velocity vector v at any point will have a horizontal component (because it was launched with an initial angle) and a vertical component (due to gravity). At the apex of the trajectory, the vertical component of the velocity is zero while the horizontal component remains unchanged. Therefore, at this highest point, the velocity vector, which is entirely horizontal, is perpendicular to the acceleration vector, which is entirely vertical. Hence, the answer is yes, velocity and acceleration are perpendicular at the apex of the trajectory.