When an object is moving in projectile motion, it follows a curved trajectory under the influence of gravity. The time it takes for the object to reach the ground is determined by the vertical component of its motion, while the horizontal component does not affect the time of descent. Consequently, regardless of the object's initial horizontal velocity or the angle of projection, the time it takes to reach the ground remains the same if the vertical displacement is the same.
The reason for this can be understood by considering the independence of horizontal and vertical motion in the absence of air resistance. When an object is launched at an angle into the air, it can be divided into two independent motions: horizontal motion at a constant velocity and vertical motion under the influence of gravity. These two motions occur simultaneously and do not directly affect each other.
Gravity acts vertically, constantly accelerating the object downward, regardless of its horizontal velocity. The object's vertical velocity increases until it reaches its peak height and then decreases as it descends. The time it takes for the object to reach the ground is determined solely by the vertical motion and is dependent on the initial vertical velocity and the height of the object.
The horizontal motion, on the other hand, remains constant throughout the object's trajectory. The horizontal velocity remains unchanged, assuming no external forces act upon the object in the horizontal direction. Consequently, the time it takes for the object to travel horizontally does not affect the time it takes to reach the ground.
Therefore, regardless of the initial horizontal velocity or launch angle, as long as the vertical displacement is the same, the time it takes for the object to reach the ground will be the same. This principle is one of the fundamental concepts in projectile motion and is known as the time of flight.