Free · Physics models
Projectile Launch, Landing and Instantaneous Velocity
Resolve launch components, landing range and instantaneous position for an ideal projectile.
- Formula & worked example
- Private in your browser
- No signup
Calculator inputs
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How to use this calculator
- Enter the known values in the units shown. Results update as you type.
- Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
- Use the worked example to check the method. Reset restores the starting fields.
Private by default
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Formula and method
A horizontal launch at 10 m/s from 4.903325 meters lands after one second and travels ten meters.
The squared launch speed equals the sum of squared perpendicular components; vertical acceleration is constant.
Worked example
Enter these known values and leave the other values blank.
- Initial velocity (V)
- 10 m/s
- Angle of launch (α)
- 0 deg
- Initial height (h)
- 4.903325 m
- Time
- .5 sec
- Time of flight (t)
- 1 sec
- Distance (d)
- 10 m
- Maximum height (h==max==)
- 4.9 m
- Initial horizontal velocity (V==x==)
- 10 m/s
- Initial vertical velocity (V==y==)
- 0 m/s
- Velocity
- 11.13744 m/s
- Horizontal velocity
- 10 m/s
- Vertical velocity
- -4.9 m/s
- Horizontal position
- 5 m
- Height
- 3.677494 m
Assumptions and limitations
- The landing plane has height zero; launch height and elapsed time are nonnegative and gravity is positive. All component, range and time inverse controls are preserved.
- A component inverse chooses the captured nonnegative square-root branch; a known signed launch angle supplies signed components through the forward relation.
- Air resistance, wind, ground obstacles and Earth curvature are omitted.
- Clear the unknown numerical field before using a supported inverse; selection controls retain their captured branches.
Common questions
What assumptions matter for this model?
The landing plane has height zero; launch height and elapsed time are nonnegative and gravity is positive. All component, range and time inverse controls are preserved.
What does this model leave out?
Air resistance, wind, ground obstacles and Earth curvature are omitted.
References
Model requirements: Launch height above the landing plane must be nonnegative. Elapsed time cannot be negative. Authored accessible explanations preserve each captured diagram mode and its geometric relationships. Restore the dimensionally consistent squared-speed identity and its norm/component inverses; the capture incorrectly equated speed to a sum of squared speeds.