Final answer:
In projectile motion, the time an object remains in the air is determined solely by its vertical motion, not its horizontal velocity. Any projectile starting with the same initial vertical speed and altitude change will have the same time of flight.
Step-by-step explanation:
The time a horizontally projected object remains in the air is determined by its vertical motion. Despite having varying initial horizontal velocities, all objects in projectile motion fall at the same acceleration due to gravity. The vertical motion dictates the time of flight, as horizontal velocity does not affect the rate at which the object descends. Hence, knowing the initial vertical velocity and the distance below the starting altitude allows us to calculate the time of flight.
For instance, a projectile with an initial vertical velocity of 14.3 m/s and landing 20.0 m below its starting altitude will spend 3.96 s in the air. This duration is the same regardless of the initial horizontal velocity because the downward motion is only influenced by gravity which is a constant 9.8 m/s2n.
Therefore, in projectile motion discussions, it is critical to separate the problem into two independent one-dimensional motions to correctly solve for time and final velocity.