Projectile Motion - Interactive Simulation

Position X: 0.00 m

Height Y: 0.00 m

Velocity: 0.00 m/s

Flight Time: 0.00 s

Max Height: 0.00 m

Range: 0.00 m

Velocity Components (vx vs vy)

Height vs Distance

Energy

Kinetic: 0.00 J

Potential: 0.00 J

Total: 0.00 J

Parameters

Initial Velocity (v₀): 50 m/s

Launch Angle (θ): 45°

Initial Height (h₀): 0 m

Gravity (g): 9.81 m/s²

Air Resistance (k): 0.00

Mass (m): 1.0 kg

X Axis Max: 500 m

Y Axis Max: 500 m

Equations of Motion

No Air Resistance: x = v₀cos(θ)t, y = h₀ + v₀sin(θ)t - ½gt²

With Air Resistance: x'' = -kvx'/m, y'' = -g - kvy'/m

Trajectory: y = h₀ + xtan(θ) - gx²/(2v₀²cos²(θ))

What is Projectile Motion?

Projectile motion is the motion of an object thrown or projected into the air, subject only to acceleration due to gravity. The path followed by a projectile is called its trajectory, which is a parabola when air resistance is neglected.

Factors Affecting Projectile Motion

Several factors influence the trajectory of a projectile: initial velocity, launch angle, initial height, gravity, and air resistance. The optimal angle for maximum range without air resistance is 45°, but this changes with air resistance and initial height.

Air Resistance Effect

Air resistance (drag) acts opposite to the velocity vector and reduces both horizontal and vertical velocity over time. This causes the projectile to fall short of its ideal range and creates an asymmetric trajectory. Compare mode lets you see this effect side-by-side.

Energy Considerations

The total mechanical energy of a projectile remains constant without air resistance, continuously transforming between kinetic and potential energy. With air resistance, energy is gradually lost to heat, causing the projectile to slow down and fall short.