Projectile Motion Calculator

Calculate the trajectory, range, maximum height, and time of flight for projectile motion. Enter initial conditions to see results and visualization.

About Projectile Motion

What is Projectile Motion?

Projectile motion is the motion of an object thrown or projected into the air, subject only to the acceleration of gravity. The object is called a projectile, and its path is called its trajectory. Examples include a thrown ball, a launched rocket, or a fired bullet (ignoring air resistance).

Key Characteristics

• The horizontal motion and vertical motion are independent of each other
• Horizontal velocity remains constant (no air resistance)
• Vertical motion experiences constant downward acceleration due to gravity
• The trajectory is a parabola (in the absence of air resistance)

Equations of Motion

Velocity Components

• Horizontal: vₓ = v₀ × cos(θ) (remains constant)
• Vertical: vᵧ = v₀ × sin(θ) - g × t (changes due to gravity)
• Magnitude: v = √(vₓ² + vᵧ²)

Optimal Launch Angle

For maximum range on level ground (h₀ = 0), the optimal launch angle is 45 degrees. However, this changes when launching from height or landing at a different elevation.

Real-World Applications

• Sports: Basketball shots, soccer kicks, golf drives
• Military: Artillery and ballistic trajectories
• Engineering: Water fountains, ski jumps
• Aerospace: Rocket trajectories, spacecraft re-entry

Assumptions

This calculator assumes:

• No air resistance (ideal projectile motion)
• Constant gravitational acceleration
• Flat horizontal surface (unless initial height specified)
• Point mass (no rotation effects)

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