Projectile Motion: The Physics of Flight

What is Projectile Motion?

Projectile motion is the movement of an object (a projectile) thrown into the air, subject only to the force of gravity and air resistance (often ignored for simplicity). The path is always a parabola.

Key Characteristics:

• Horizontal velocity (Vₓ) is constant.
• Vertical velocity (Vᵧ) changes due to gravity.
• Acceleration is constant: Aᵧ = -9.8 m/s².

Analyzing Components and Key Equations

Horizontal Motion (X)

No force acts horizontally (ignoring air resistance). This means acceleration (Aₓ) is zero, and the velocity (Vₓ) remains constant throughout the flight.

    Vₓ = V₀ cos(θ)

    Δx = Vₓ * t

    Aₓ = 0

Vertical Motion (Y)

The projectile experiences constant downward acceleration due to gravity (g). This is standard kinematic motion, independent of horizontal motion.

    Vᵧ = V₀ sin(θ)

    Aᵧ = -g (-9.8 m/s²)

    Vᵧf = Vᵧi + Aᵧt

    Δy = Vᵧi * t + 0.5 * Aᵧ * t²

Interactive Projectile Motion Simulator

Settings (Initial Velocity)

Velocity (m/s): Angle (°):

Key Parameters: Range and Maximum Height

Range (Δx)

The total horizontal distance the projectile travels from launch until it returns to the same vertical level. Depends heavily on V₀ and launch angle.

R = (V₀² sin(2θ)) / g

Maximum Height (H)

The highest vertical point reached. At this point, the vertical velocity (Vᵧ) is momentarily zero.

H = (V₀² sin²(θ)) / (2g)

Optimal Angle

For maximum horizontal range, the optimal launch angle (on level ground) is 45 degrees.

θ = 45°

Time of Flight (T)

The total time the projectile remains in the air. This is determined solely by the vertical component of the motion.

T = (2V₀ sin(θ)) / g