If you need horizontal velocity (vₓ), vertical velocity (vᵧ) and ymax and you already have angle of launch (α), initial height (h₀), velocity, cos and sin, this calculator does the substitution for you. It suits a quick check, a homework answer you want to confirm, or any figure you need to sanity test.
What Is the Trajectory Projectile Motion Calculator?
This trajectory projectile motion calculator is for the kind of problem where you know the physical quantities but not the number you need. It turns angle of launch (α), initial height (h₀), velocity, cos and sin into horizontal velocity (vₓ), vertical velocity (vᵧ) and ymax.
Physics calculations go wrong in predictable ways, usually through mixing units or dropping a digit. Work through the result one step at a time and check that the figures are the size you would expect at each stage.
How the Trajectory Projectile Motion Physics Works
The relationship is applied step by step, and each step is a standard piece of physics rather than a single opaque formula. That means you can check the intermediate values against what the theory predicts, which is usually faster than checking only the final answer.
Keep every value in the same unit system throughout the calculation. Mixing metres and feet part way through is the single most common reason a correct formula gives a wrong answer.
Units, Assumptions and the Limits of the Model
The calculation assumes ideal conditions: no air resistance, no heat loss, and dimensions that do not change while you work. Those assumptions are reasonable for most classroom and engineering estimates, and unreasonable for anything more precise.
Where a value is a rate, it has to be quoted for the same period as everything else. A per-hour figure cannot be combined with a per-day figure without converting one of them first.
A Worked Example
Working through an example, with angle of launch (α) set to 10, initial height (h₀) set to 5, velocity set to 2, the calculator returns horizontal velocity (vₓ) of -1.678143, and vertical velocity (vᵧ) of -1.088042, and ymax of 5.06036. Substitute your own figures and the same steps produce the same kind of answer.
Frequently Asked Questions
What do I need to work out horizontal velocity (vₓ)?
Enter angle of launch (α), initial height (h₀), velocity, cos and sin. The calculator then works through the relationship and reports horizontal velocity (vₓ), vertical velocity (vᵧ) and ymax.
What does the trajectory projectile motion actually calculate?
It takes angle of launch (α), initial height (h₀), velocity, cos and sin and converts them into horizontal velocity (vₓ), vertical velocity (vᵧ) and ymax using the standard relationship for this problem. Each step is applied in turn, so every output is traceable back to the numbers you typed in.
How should I enter angle of launch (α)?
Use the value you actually have, in the unit shown next to the field. Enter every value in the same unit system. The calculator assumes the figures you supply are consistent, so it cannot correct a mistake that happens before the calculation starts.
Can I use this for a quick estimate as well as a precise answer?
Yes. The calculator is built for quick checks, so round your inputs to a sensible number of significant figures and the result will be just as useful. If you need more precision, keep the same method and add digits to the inputs rather than adjusting the method itself.
Do I have to fill in every field?
Only the fields a particular result depends on. If you leave one blank, the results that need it simply show a note instead of a number, and everything else still works.