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Projectile Motion Simulator

Visualize and calculate projectile motion in real time

Visualize Projectile Motion in Real Time

Experiment with launch angle, velocity, gravity and air resistance, and instantly view the trajectory, live graphs and calculated physics values.

📈 Trajectory View

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⌚
Time of Flight
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↑
Maximum Height
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↔
Horizontal Range
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⚡
Current Speed
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💥
Impact Speed
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📍
Current Position
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↔
Horizontal Distance
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↕
Vertical Distance
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🍴
Potential Energy
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🏒
Kinetic Energy
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⚛
Total Mechanical Energy
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📊 Trajectory Graph

Projectile Motion Formulas

The core equations driving this simulation

Time of Flight

T = (u sinθ + √((u sinθ)² + 2gh)) / g

u = initial velocity, θ = launch angle, g = gravity, h = initial height. Unit: seconds (s).

Example: u=25 m/s, θ=45°, h=0 → T ≈ 3.61 s

Maximum Height

H₀ = h + (u² sin²θ) / (2g)

Height reached above the ground at the apex of the trajectory. Unit: meters (m).

Example: u=25 m/s, θ=45° → H₀ ≈ 15.92 m

Horizontal Range

R = u cosθ × T

Total horizontal distance travelled before landing. Unit: meters (m).

Example: u=25 m/s, θ=45°, h=0 → R ≈ 63.71 m

Horizontal Velocity

vₓ = u cosθ

Constant throughout flight when air resistance is off. Unit: m/s.

Example: u=25 m/s, θ=45° → vₓ ≈ 17.68 m/s

Vertical Velocity

vᶟ(t) = u sinθ − g t

Changes over time under gravity. Zero at the apex. Unit: m/s.

Example: u=25 m/s, θ=45°, t=1s → vᶟ ≈ 7.87 m/s

Position Equations

x(t)=vₓt    y(t)=h+vᶟt−½gt²

Full parametric position of the projectile at any time t. Unit: meters (m).

Used every animation frame to plot the trajectory.

Step-by-Step Solution

A worked solution generated from your current parameters

Click “Generate Solution” to see a full worked example using your current launch parameters.

Unit Converter

Quickly convert between common projectile motion units

Speed

→

25 m/s = 90 km/h

Angle

→

45° = 0.7854 rad

Length

→

10 m = 32.81 ft

Physics Challenge Mode

Test your intuition with mini physics challenges

Hit the Target

Adjust your launch parameters and hit the target flag shown on the trajectory view, then press Launch.

0 pts

No attempt yet

Learn the Physics

Core concepts behind projectile motion

Projectile Motion
Projectile motion describes the curved path traced by an object launched into the air and acted on only by gravity, and optionally air resistance. The motion can be split into independent horizontal and vertical components.
Gravity
Gravity is the constant downward acceleration acting on the projectile. It curves the otherwise straight path of the object into a parabola on a planet with no air resistance.
Velocity Components
Initial velocity u at angle θ splits into a horizontal component u cosθ and a vertical component u sinθ, which are analyzed separately.
Horizontal Motion
With no air resistance, horizontal velocity stays constant since no horizontal force acts on the projectile, so horizontal distance grows linearly with time.
Vertical Motion
Vertical velocity decreases due to gravity until it reaches zero at the apex, then increases in the downward direction as the projectile falls.
Launch Angle
The launch angle controls the balance between horizontal and vertical velocity. On flat ground with no drag, 45° produces the maximum range.
Air Resistance
Air resistance is a drag force that opposes motion and grows with speed. It reduces range and maximum height and makes the trajectory asymmetric.
Energy Conservation
Without air resistance, total mechanical energy (potential plus kinetic) stays constant throughout the flight. With air resistance, some energy is lost to drag.
Momentum
Momentum is mass times velocity. Horizontal momentum is conserved without air resistance, while vertical momentum changes continuously due to the force of gravity.

Frequently Asked Questions

What launch angle gives the maximum range?
On flat ground with no air resistance, 45 degrees gives the maximum horizontal range for a given launch speed.
Does air resistance change the optimal launch angle?
Yes, with air resistance the optimal angle for maximum range is usually lower than 45 degrees because drag increases with speed.
Why does the projectile land at the same speed it launched with on level ground?
Without air resistance, energy is conserved, so when the projectile returns to launch height its speed equals the initial speed, just with a reversed vertical direction.