Physics
Projectile Scenario Comparison Calculator
Compare two ideal projectile scenarios with independent speeds and angles, shared height and gravity, complete trajectory metrics, and target-distance margins.
A horizontal velocity-
A vertical velocity-
A flight time-
A horizontal range-
A maximum future height (m)-
B horizontal velocity-
B vertical velocity-
B flight time-
B horizontal range-
B maximum future height (m)-
B minus A range-
A range minus target-
B range minus target-
Decision view
Two ideal projectile trajectory comparison
Two ideal projectile trajectory comparisonScenario A and B paths, apexes, ranges, and the shared target distance are overlaid on one coordinate system.
Exact scenario comparisonScenario B angle changes while all other entered assumptions remain constant.
| Scenario B angle | A horizontal velocity | A vertical velocity | A flight time | A horizontal range | A maximum future height (m) | B horizontal velocity | B vertical velocity | B flight time | B horizontal range | B maximum future height (m) | B minus A range | A range minus target | B range minus target |
|---|
How to use Projectile Scenario Comparison Calculator
- Enter speed and angle for scenario A.
- Enter speed and angle for scenario B.
- Set their shared launch height, gravity, and target distance.
- Compare the two live trajectories and exact result rows.
Calculator guide
Understanding Projectile Scenario Comparison Calculator
Two projectile launches can share height and gravity yet differ substantially in range, flight time, apex, and target clearance because speed and angle affect different velocity components. This comparison solves both paths independently before calculating any difference.
Calculation method
How the calculation works
Solve two independent ideal projectile scenarios under the same gravity and height before comparing range, time, apex, and target-distance margins. Both paths share one origin and gravity, making the signed range difference directly comparable. Apply the component and positive-impact equations separately to scenarios A and B, then subtract their ranges and compare each range with the entered target distance.
Detailed calculation process
Solve two projectile paths before comparing their target margins
Scenario A uses 28 m/s at 35°, scenario B uses 32 m/s at 45°, and both start at 1.2 m under standard gravity.
General formula: for i in {A,B}: v_xi = v_i cos(theta_i)v_yi = v_i sin(theta_i)t_i = [v_yi + sqrt(v_yi^2 + 2gh_0)]/gR_i = v_xi t_iH_i = h_0 + v_yi^2/(2g)DeltaR = R_B - R_A Each scenario must first produce its own component velocities, flight time, range, and apex. Only then are ranges and target margins subtracted, preventing one scenario's time or angle from leaking into the other.
What each symbol means
Worked substitution with the default inputs
Under the defaults, B travels 28.805 m farther, stays aloft 1.319 s longer, and peaks 12.954 m higher than A.
Scenario comparison
Overlay both ideal trajectories on one coordinate plane
Two function curves show where speed and angle alter range and apex while a shared target line anchors the comparison.
Worked situations
Practical examples
- A reaches 76.801 m while B reaches 105.605 m.
- Both scenarios clear the 70 m range target.
- B's higher vertical component produces a much higher apex.
Better inputs
Useful tips
- Change one scenario input at a time when testing sensitivity.
- Compare components as well as final range.
- Use identical environmental assumptions for a fair ideal comparison.
Before relying on the result
Limitations and common mistakes
- Both scenarios exclude aerodynamic effects and assume point masses.
- The same gravity and launch height are imposed on both paths.
- A longer ideal range does not establish real-world accuracy or safety.
Reference
Key terms
- Scenario margin
- Modeled range minus the entered target distance.
- Range difference
- Scenario B range minus scenario A range.
- Shared assumption
- A value, such as gravity, applied identically to both paths.
- Trajectory overlay
- Two paths plotted on the same axes for direct comparison.
Important note
Calculated from the entered values using the displayed physical model. Confirm that its assumptions, units, boundary conditions, and safety limits match the application.
Frequently asked questions
Why can horizontal velocities be similar but ranges differ?
Flight time also matters; B's larger vertical component keeps it aloft longer.
Is 45° always the longest-range angle?
Only under restricted ideal assumptions, especially zero launch height and no drag.
What does a negative target margin mean?
The modeled range ends before the entered target distance.
Are the two paths evaluated independently?
Yes. Each uses its own speed and angle.