How does the vertical component of a projectile's motion compare with the motion of vertical free fall when air resistance is negligible?
Choices are: a. greater than that of free fall, b. less than that of free fall, c. identical to that of free fall, d. it cannot be determined.
The correct answer is c, identical to free fall. This is true because the only force acting on an object in the vertical direction is the gravitational force. Whether an object is moving upward at some initial velocity, or falling downward, the acceleration of gravity acting on the object is identical. For vertical motion, the velocity is constantly changing - either increasing if the object is falling or decreasing as the object is rising. On the other hand, the horizontal component of an object is considered to be a constant velocity (ignoring air resistance)
When the air resistance is negligible the vertical component of a projectile's motion is identical to the motion of vertical free fall.
Here please note that the expression "free fall" also includes the rise, which may be considered as negative free fall.
However if we take the air resistance as significant then the relationship becomes complex, as the air resistance changes with the total speed. Thus the acceleration itself varies, being maximum at the highest point of the projectile, when the vertical speed is 0. It must also be noted that if the air resistance is significant then we cannot assume the horizontal component of the speed to be constant. The horizontal speed will reduce as the projectile moves forward horizontally. This negative acceleration will be maximum when the projectile is launched.