1: Break down the motion into x, y, and z components. 2: Analyze each component independently using 1D kinematic equations. 3: Combine the components to determine the overall motion.

1: Resolve the initial velocity into horizontal ($v_{0x} = v_0 cos( heta)$) and vertical ($v_{0y} = v_0 sin( heta)$) components. 2: Analyze vertical motion using kinematic equations with $a = -g$. 3: Analyze horizontal motion using constant velocity ($v_x = v_{0x}$). 4: Use time as the common variable between horizontal and vertical motion.

1: Recognize that the vertical velocity ($v_y$) is zero at the maximum height. 2: Use the kinematic equation $v_y = v_{0y} + at$ to find the time to reach the maximum height. 3: Use the kinematic equation $y = v_{0y}t + frac{1}{2}at^2$ to find the maximum height.

1: Find the total time of flight (twice the time to reach maximum height). 2: Use the equation $x = v_{0x}t$ to calculate the horizontal range, where $v_{0x}$ is the initial horizontal velocity and t is the total time of flight.

1: Determine the initial vertical velocity ($v_{0y}$). 2: Use the kinematic equation $v_y = v_{0y} + at$ to find the time to reach the maximum height (where $v_y = 0$). 3: Double the time to reach the maximum height to find the total time of flight (assuming launch and landing at the same height).

Horizontal Motion: Constant velocity, zero acceleration. | Vertical Motion: Constant acceleration (due to gravity), changing velocity.

Velocity: Can change in both magnitude and direction. | Acceleration: Can vary between dimensions and may be non-uniform.

Launch Point: Non-zero vertical and horizontal velocity components. | Maximum Height: Zero vertical velocity, non-zero horizontal velocity.

Quantitative Analysis: Involves precise numerical calculations and measurements (common in 2D). | Qualitative Analysis: Focuses on descriptions and observations without specific numerical values (may be used in 3D).

Horizontal Motion: Gravity has no direct effect (assuming no air resistance). | Vertical Motion: Gravity causes constant downward acceleration.

Motion in more than one dimension (e.g., 2D or 3D space), requiring analysis of motion components along different axes.

The process of breaking down a vector (like velocity or acceleration) into its components along different axes (typically x, y, and z) to analyze motion in each direction independently.

The motion of an object thrown or projected into the air, subject to only the acceleration of gravity (ignoring air resistance).

The path followed by a projectile, typically a parabola under the influence of gravity (assuming constant gravitational acceleration and negligible air resistance).

The horizontal distance traveled by a projectile from its launch point to the point where it returns to the same vertical level.

The horizontal component of velocity, which remains constant throughout the projectile's flight because there is no horizontal acceleration.