Horizontal projectile motion occurs when an object is launched with an initial velocity that is purely horizontal. The projectile then moves under the influence of gravity alone, creating a characteristic parabolic path. The horizontal velocity remains constant while the vertical velocity increases due to gravitational acceleration.
The motion of a horizontal projectile can be analyzed by breaking it into two independent components. The horizontal component maintains constant velocity equal to the initial launch velocity. The vertical component starts from zero and increases linearly with time due to gravitational acceleration. These two motions are completely independent of each other.
The trajectory of a horizontal projectile follows a parabolic path described by the equation y equals g over 2 v naught squared times x squared. The time of flight depends only on the initial height and gravity, not on the horizontal velocity. However, the horizontal range increases with initial velocity, as it equals v naught times the square root of 2h over g.
Let's solve a practical example. A ball is thrown horizontally from a 20 meter high cliff with an initial velocity of 15 meters per second. First, we calculate the time of flight using the square root of 2h over g, which gives us 2.02 seconds. The horizontal range is velocity times time, equaling 30.3 meters. Finally, the final velocity combines horizontal and vertical components, resulting in 25.1 meters per second.
To summarize what we have learned about horizontal projectile motion: it combines constant horizontal velocity with accelerated vertical motion due to gravity. These two components are completely independent of each other. The time of flight depends only on the initial height, while the horizontal range depends on both initial velocity and time of flight. Understanding these principles helps us analyze many real-world projectile scenarios.