Projectile motion problems are solved by separating the motion into horizontal and vertical components because they are independent of each other, using kinematic equations to analyze each component's motion, and finally recombining them to understand the full trajectory.
When solving a projectile motion problem, it is crucial to separate the motion into horizontal and vertical components because these motions are independent of each other. The horizontal motion (along the x-axis) and the vertical motion (along the y-axis) are analyzed using their respective kinematic equations, which consider the initial velocity components, displacements, and acceleration due to gravity for the vertical motion.
For the horizontal direction, labeled as the x-axis, the velocity is constant as there is no acceleration (assuming negligible air resistance). For the vertical direction, or y-axis, the motion is affected by gravity, providing a constant acceleration downwards. By resolving the motion and analyzing these components separately using vector addition, we can understand the complete motion of the projectile.
To summarize, projectile motion problems are solved by breaking down the motion into independent x (horizontal) and y (vertical) components. Each component is analyzed using kinematic equations, considering factors like initial velocity, acceleration (only in the vertical component due to gravity), and displacement to recombine for a full analysis of the projectile's trajectory.