At the maximum height of a projectile's trajectory, the following relationships hold regarding acceleration and velocity:
Velocity: At the maximum height, the velocity of the projectile becomes zero. This occurs because the projectile reaches its highest point and momentarily comes to a stop before starting to descend. The direction of the velocity also changes from upward to downward.
Acceleration: The acceleration at the maximum height remains constant and is equal to the acceleration due to gravity (g). The acceleration due to gravity acts vertically downward throughout the trajectory of the projectile, including at the maximum height. However, it's important to note that the magnitude of the velocity is zero at the maximum height, but the acceleration due to gravity is still acting on the object.