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Horizontal Projectile Motion Calculator — result sheet
Calculate flight time, horizontal range, and impact speed for an object launched horizontally from a height.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: Time to ground t = √(2h/g). Horizontal range x = horizontal speed × t. Vertical impact speed = g × t. Impact speed magnitude = √(horizontal speed² + vertical impact speed²).
This is the ideal horizontal-launch model: zero initial vertical velocity, constant gravity, level landing reference, and no air resistance. It complements an angled projectile model rather than replacing it.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Launch height — m; minimum 1.0E-6; maximum 1000000
- Horizontal launch speed — m/s; minimum 0; maximum 1000000
- Gravitational acceleration — m/s²; minimum 1.0E-6; maximum 1000
Worked example
| Input | Value |
|---|---|
| Launch height | 20 |
| Horizontal launch speed | 10 |
| Gravitational acceleration | 9.80665 |
From 20 m with a 10 m/s horizontal speed, ideal flight time is about 2.0193 s, range about 20.193 m, and impact speed about 22.185 m/s.
Assumptions and limits
- The object begins with zero vertical velocity.
- The entered launch height is measured above the landing level.
- Gravity is constant throughout the flight.
- Horizontal acceleration is zero in the ideal model.
- Air resistance, wind, lift, rotation, and shape are not modeled.
- The horizontal range is measured from the launch point to the landing point.
- Impact speed combines perpendicular horizontal and vertical components.
- The result does not identify a safe release height, landing zone, or operating procedure.
- A zero horizontal speed still produces a vertical drop with zero horizontal range.
- For a real object, terrain, drag, and launch mechanics can materially change the path.
Calculator note
Source and methodology
Use the official WorldCalculate methodology policy for the source, formula, precision, and boundary standards behind this calculator.
Planning estimate, not financial, medical, legal, or professional advice. © WorldCalculate — reuse with attribution. Built and curated by Hassan ALRowaie.
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