Final answer:
A projectile can have a horizontal displacement even though its vertical displacement is zero because the horizontal and vertical motions are independent of each other. The horizontal displacement is determined by the projectile's horizontal velocity and time of flight, while the vertical displacement is affected by gravity and initial vertical velocity.
Step-by-step explanation:
The reason a projectile can have a horizontal displacement even though its vertical displacement is zero is because the horizontal and vertical motions are independent of each other. This means that the projectile can have a constant horizontal velocity while its vertical displacement remains zero. For example, if you throw a ball straight ahead with a certain horizontal velocity, the ball will continue to move horizontally at that velocity even though it has no vertical displacement.
This is due to the fact that in the absence of air resistance (assuming negligible air resistance), the horizontal motion of a projectile remains constant. The horizontal displacement of the projectile is determined by its horizontal velocity and the time of flight. On the other hand, the vertical motion is affected by gravity and the initial vertical velocity of the projectile. In the case where the vertical displacement is zero, it means that the initial vertical velocity is zero and the projectile does not move up or down vertically.
Therefore, option a) is incorrect because it is not necessary for the horizontal velocity to be greater than the vertical velocity for a projectile to have a horizontal displacement even with a zero vertical displacement.