What Is Projectile Motion?
Projectile motion describes the curved path an object follows when launched into the air at an angle, influenced only by gravity. It's a fundamental concept in physics that applies to everything from sports and fireworks to engineering and space exploration.
The Physics Behind It
Projectile motion combines two independent motions that work simultaneously:
Constant Velocity
- No acceleration
- Uniform motion
- Distance = velocity × time
Accelerated Motion
- Gravity acceleration (g = 9.81 m/s²)
- Velocity changes continuously
- Forms parabolic curve
The trajectory forms a parabolic curve, governed by these fundamental equations:
// Horizontal position
x(t) = v₀ · cos(θ) · t
// Vertical position
y(t) = h₀ + v₀ · sin(θ) · t − ½ · g · t²
Where:
v₀ = initial velocity
θ = launch angle
h₀ = initial height
g = gravitational acceleration
t = time- 1. What Is Projectile Motion?
- 2. How to Use This Calculator
- 3. Features
- 4. Frequently Asked Questions
- 4.1. What is the best angle for maximum range?
- 4.2. Does this calculator account for air resistance?
- 4.3. Why does the same velocity produce different ranges on different planets?
- 4.4. How is impact velocity calculated?
- 4.5. Can I use this for objects launched from a height?
- 4.6. Is my data stored or sent anywhere?
How to Use This Calculator
Enter Launch Parameters
Fill in the input fields on the left panel with your launch conditions:
- Initial Velocity (v₀) — the speed at which the object is launched
- Launch Angle (θ) — the angle above the horizontal (use the slider or type a value)
- Initial Height (h₀) — the height from which the object is launched (0 for ground level)
- Gravity (g) — select a planet preset or enter a custom value
View Results
Results update instantly as you change any parameter. The calculator displays:
Range
Max Height
Flight Time
Impact Velocity
Explore the Trajectory
The interactive canvas displays the parabolic path with key points marked: launch, peak, and landing. Hover over the curve to see the exact position, time, and velocity at any point along the trajectory.
Compare Trajectories
Click the + button to add up to 3 trajectories. Each trajectory is drawn with a different color, making it easy to compare different launch configurations side by side.
Features
Trajectory Visualization
Watch the parabolic path drawn on an interactive canvas with coordinate grid and axis labels.
- Launch point marker
- Peak (highest point) indicator
- Landing point display
- Dashed guide lines for reference
Multi-Trajectory Comparison
Add up to 3 trajectories simultaneously with different colors (blue, amber, green).
- Toggle individual visibility
- Remove trajectories easily
- Compare angles and velocities
- Analyze gravity effects
Planetary Gravity Presets
Quickly switch between gravitational acceleration values for different celestial bodies.
- Earth — 9.81 m/s²
- Moon — 1.62 m/s²
- Mars — 3.72 m/s²
- Jupiter — 24.79 m/s²
Unit Conversion
Switch between different measurement units without losing your data.
- Velocity: m/s, km/h, ft/s
- Distance: meters, feet
- Angle: degrees, radians
Interactive Tooltip
Hover over (or touch on mobile) any point along the trajectory curve.
- Exact horizontal distance
- Current height
- Elapsed time
- Velocity at that position
Optimal Angle
Automatically computes the optimal launch angle for maximum range.
- 45° on flat ground
- Adjusts for elevated launches
- Real-time calculation
- Displayed automatically
Frequently Asked Questions
What is the best angle for maximum range?
On flat ground (h₀ = 0), the optimal angle is 45°. This gives the perfect balance between horizontal distance and time in the air.
When launching from a height above the ground, the optimal angle is slightly less than 45° — the calculator shows the exact value automatically based on your initial height.
Does this calculator account for air resistance?
No, this calculator uses the ideal projectile motion model, which assumes:
- No air resistance (drag)
- Constant gravitational acceleration
- No wind effects
- Vacuum conditions
Why does the same velocity produce different ranges on different planets?
Range depends directly on gravitational acceleration. The relationship works like this:
Moon (1.62 m/s²)
- Projectile stays airborne longer
- Travels much farther
- ~6× Earth's range
Jupiter (24.79 m/s²)
- Pulled down quickly
- Much shorter range
- ~40% of Earth's range
Lower gravity = longer flight time = greater range for the same initial velocity and angle.
How is impact velocity calculated?
Impact velocity is the speed at which the projectile hits the ground. It's calculated by combining two velocity components:
Horizontal Component
vₓ = v₀ · cos(θ)Vertical Component
vᵧ = v₀ · sin(θ) − g · tThe final impact speed is the magnitude of the combined velocity vector at landing time:
v_impact = √(vₓ² + vᵧ²)Can I use this for objects launched from a height?
Yes, absolutely! Set the Initial Height (h₀) to the launch height in meters or feet.
The calculator will automatically account for the extra height when computing:
- Extended flight time
- Increased range
- Higher impact velocity
- Adjusted optimal angle
Is my data stored or sent anywhere?
No. Your privacy is fully protected.
All calculations are performed entirely in your browser using JavaScript. This means:
- No data is uploaded to any server
- No tracking or analytics on your inputs
- Works completely offline once loaded
- 100% client-side processing
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