Final answer:
Option B) 45 m/s is correct because the horizontal velocity of a projectile remains constant in projectile motion unless there's horizontal acceleration, which is not present in this scenario.
Step-by-step explanation:
The question is concerned with understanding the properties of projectile motion in Physics, specifically relating to the horizontal component of velocity of a cannonball after it has been fired. In the absence of air resistance, the horizontal velocity of a projectile remains constant because there is no horizontal acceleration acting on it. Therefore, since the cannonball was launched with an initial horizontal velocity of 45 m/s west, the magnitude of the cannonball's horizontal velocity at three seconds will still be 45 m/s.
Option B) 45 m/s is the correct answer to the question of what the magnitude of the cannonball's horizontal velocity will be at three seconds after it has been fired.