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In our problem, kinematic analysis helps us understand the motion of the ball both before and after the collision. By breaking down the velocity of the ball into components, we can visualize how each affects the outcome of the collision.
Before the ball hits the wall, it travels at a certain velocity. This velocity has two components:

• Normal to the wall (perpendicular).
• Parallel to the wall.

Since the ball is thrown at a 45-degree angle to the line OA, both components play significant roles. The angle of 45 degrees indicates that these components are equal in magnitude.
The kinematic analysis becomes crucial when observing the sudden stop of the normal velocity component. This change is indicative of energy loss through the collision. Each component can be calculated using trigonometry, which allows us to further unravel the behavior of the ball during its journey.

Collision mechanics deal with what happens during the impact between two bodies—in this case, a ball and the wall. Here, understanding the nature of the impact is vital for determining the coefficient of restitution.
During the collision, mechanical energy is partially lost, especially in real-world scenarios. The coefficient of restitution (e) quantifies the elasticity of the collision:

• If \(e = 1\), the collision is perfectly elastic, meaning no kinetic energy is lost.
• If \(e = 0\), the collision is perfectly inelastic, which means the bodies do not rebound apart.

In our problem, since the ball rebounds such that it travels parallel to OA, it signifies that all energy in the normal direction is lost, representing an inelastic collision with \(e = 0\). Understanding this ratio provides insight into the dynamics occurring during these impactful events.

The angle of incidence is a key concept to understanding the motion of the ball as it approaches and makes contact with the wall. It directly influences the behavior of the ball upon rebound.
This angle—between the trajectory of the ball and a line perpendicular to the surface—determines how the velocity components are distributed. In the given problem, this angle of 45 degrees (an acute angle) results in equal contributions from the normal and tangential velocity components at the point of contact.
The angle of incidence not only affects how the ball hits the wall but also defines the pathway the ball takes after bouncing off. Since the ball rebounds at 90 degrees to the surface, it implies the absence of a normal component post-collision. Hence, the angle of incidence governs how momentum and energy are handled in such scenarios and is pivotal to predicting post-impact trajectories.