Final Answer:
As the cannonball flies through the air with its velocity vector components changed from total to Vx and Vy, you'll notice that Vx remains constant throughout the projectile's motion while Vy changes due to the influence of gravity.
Step-by-step explanation:
When breaking down the velocity vector into its horizontal (Vx) and vertical (Vy) components, Vx represents the constant horizontal velocity of the projectile. This component remains unchanged because in the absence of external horizontal forces (like air resistance), there is no acceleration acting on the object in the horizontal direction according to Newton's first law of motion. Therefore, Vx remains a constant value throughout the cannonball's flight.
On the other hand, Vy, representing the vertical component of velocity, changes due to the force of gravity acting upon the cannonball. At the moment of launch, Vy is at its initial magnitude. As the cannonball moves upwards against gravity, Vy decreases until it reaches its maximum height, where it becomes zero. Subsequently, as the cannonball falls back down, Vy increases in magnitude due to the acceleration caused by gravity, but this time in the opposite direction of the initial launch.
The changes in Vy occur because of the effect of gravity, which imparts a vertical acceleration of -9.81 m/s^2 (assuming Earth's gravity) to the cannonball throughout its trajectory. The horizontal component, Vx, remains unaffected by this gravitational force and stays constant as the cannonball moves through the air. Therefore, the change in Vy and the constancy of Vx illustrate the independent behavior of the horizontal and vertical motion components of the cannonball.