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.

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).

The range increases up to a launch angle of 45°, then decreases for angles greater than 45° (assuming level ground).

Gravity causes a constant downward acceleration, decreasing the upward vertical velocity until it reaches zero at the maximum height, then increasing the downward vertical velocity.

Increasing the initial velocity increases the range of the projectile (assuming all other factors remain constant).

The time of flight increases because it takes longer for gravity to bring the projectile back down.

The range and maximum height of the projectile will decrease, and the time of flight will be shorter.