Projectile Motion: every formula, derived — and six problems solved step by step
Each formula has its own complete derivation. Each problem is solved one step at a time; the picture grows with every step to show why that formula was needed and how its answer leads to the next one.
Conventions used everywhere on this page
g = 9.81 m/s², air resistance ignored.
Case A (horizontal launch from a height): down is positive for vertical quantities, so the vertical acceleration is +g.
Cases B and C (launch at an angle): up is positive, so the vertical acceleration is −g. In Case C the origin is the ground under the launch point.
The calculator keeps full precision between steps; numbers shown are rounded.
1 · The formula list
Tap Derivation on any card to see every step. Formula IDs (like A5) are the same ones used in the Session 4 notes and in the worked problems below.
2 · Case A: horizontal launch from a height
3 · Case B: launch at an angle, landing at the same height