Final answer:
The vertical component of a projectile's motion when air resistance is negligible is identical to that of free fall, due to the constant acceleration caused by gravity.
Step-by-step explanation:
The vertical component of a projectile's motion with negligible air resistance is identical to that of free fall. This is because the only force acting on the projectile in the vertical direction is gravity, which causes the projectile to accelerate downward at a constant rate, just like an object in free fall. The horizontal and vertical motions are independent of one another, therefore the horizontal motion does not affect the vertical acceleration caused by gravity.
During projectile motion, at the highest point of its trajectory, the vertical velocity is zero, which is consistent with the behavior of an object thrown straight up into the air where its vertical velocity is also zero at the peak. However, after that point, the vertical component of the projectile's velocity increases again and in the opposite direction, under the constant acceleration due to gravity. The independence of the horizontal and vertical motions ensures that air resistance being negligible, projectile motion behaves like free fall in the vertical direction.