Free · Physics models
Projectile Components and Flight Path
Connect launch speed and angle with flight duration, height and instantaneous velocity without air resistance.
- Formula & worked example
- Private in your browser
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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.
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Formula and method
Launching horizontally at 10 m/s from 4.903325 meters above the landing plane gives a one-second flight and a ten-meter range.
Resolve launch velocity into perpendicular components; integrate constant vertical acceleration and solve the nonnegative landing-time root.
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 (hmax)
- 4.9 m
- Velocity
- 11.13744 m/s
Assumptions and limitations
- Gravity is constant and downward; the ground landing plane is height zero. Initial height is nonnegative and time is measured from launch.
- The angle is measured from horizontal, and the root chooses future landing. Show-more preserves the component and position controls.
- Air resistance, curvature of Earth, wind and obstacles 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?
Gravity is constant and downward; the ground landing plane is height zero. Initial height is nonnegative and time is measured from launch.
What does this model leave out?
Air resistance, curvature of Earth, wind and obstacles 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.