Final answer:
The critical assumption is that the initial vertical velocity of a projectile launched horizontally is zero.
Step-by-step explanation:
The critical assumption that must be made about the initial vertical velocity of a projectile launched horizontally is that it is zero.
When a projectile is launched horizontally, it means that it is only experiencing the horizontal motion, while the vertical motion is solely due to the force of gravity. Therefore, the initial vertical velocity is zero.
For example, if you throw a ball horizontally from a tall building, its initial vertical velocity is zero because it is not being propelled upwards.