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Kinematics is the branch of physics that deals with the motion of objects. It describes how objects move through space over time. In the context of projectile motion, kinematics focuses on two main components: horizontal motion and vertical motion. Each component can be analyzed separately to understand the overall trajectory of the projectile.

In projectile motion, the horizontal and vertical motions are independent of one another. This means that changes in velocity in one direction do not affect the velocity in another direction. In this exercise, the baseball moves horizontally with constant velocity since there is no horizontal acceleration, while the vertical motion is affected by gravity.
This horizontal-vertical separation simplifies the study of projectile motion, as you can tackle each direction individually. The key is to keep in mind that calculations for horizontal motion typically involve constant velocity, while calculations for vertical motion account for gravitational acceleration.

Gravity plays a crucial role in projectile motion by influencing the vertical motion of the object. Specifically, gravity is the force that accelerates the object downward at a constant rate. This rate of acceleration is often denoted by the symbol \(g\) and is approximately equal to \(9.8 \, \text{m/s}^2\) on the surface of the Earth.

In this exercise, the baseball falls freely under the influence of gravity while it moves horizontally towards the batter. This means that while the baseball maintains a constant speed in the horizontal direction, it gains speed in the vertical direction due to gravity.
It's essential to understand that the vertical displacement an object experiences due to gravity increases with time. This is because the longer an object is under the influence of gravity, the faster it moves downward, resulting in a greater distance fallen. This concept explains why the ball falls a longer distance during the second half of its flight compared to the first half, as highlighted in this exercise.

Horizontal motion in projectile problems like this one involves an object moving with constant velocity, meaning there is no horizontal acceleration. For the baseball, its speed in the horizontal direction remains constant at \(44.72 \, \text{m/s}\), as calculated from the initial speed given in kilometers per hour.

Because there is no horizontal acceleration, we use a straightforward formula to calculate the time the ball takes to cover a certain distance: \(t = \frac{d}{v}\), where \(t\) is time, \(d\) is horizontal distance, and \(v\) is horizontal velocity.
This formula allows us to conclude that the time taken to cover the first half of the distance is exactly the same as for the second half, since the speeds are identical throughout the travel.

• First half time: \(0.2047\) seconds
• Second half time: \(0.2047\) seconds

Understanding this aspect of constant horizontal motion helps clarify why the time distributions are equal in both halves, despite differences in how far and fast it falls vertically.