Projectile Motion as Two Independent Motions
The horizontal and vertical motions of a projectile are worked separately: constant velocity across, uniform acceleration down, sharing nothing but the time. A ball rolled off a bench becomes two one-dimensional problems joined by t.
What a learner can do afterwards
- Keeps a separate list of u, v, a, s and t for the horizontal and the vertical direction
- Uses time as the only quantity the two directions share
- Predicts where a ball rolled off a bench lands and says why its mass does not appear
1 · Read
Keep two lists, one per direction, sharing only the time. Sideways there is no acceleration, so the sideways speed never changes, since nothing pushes sideways. Vertical motion has g downward, so only the vertical speed grows downward. Mass appears in neither list.
Time is the only quantity both directions share: solve one direction for t, then carry it across. A ball rolled off a 1.25 m bench at 2 metres per second sideways falls for about half a second, since 1.25 is 4.9 t squared. Sideways distance is speed times time, so it lands about 1 m out.
Mass never appears because gravity accelerates all masses equally, and no mass term enters the sideways motion either. A heavy ball and a light ball rolled off together at the same speed land together, side by side.
Never mix the lists: bench height belongs in the vertical list, sideways speed in the horizontal one. Write u, v, a, s and t twice, once per direction, and circle the shared t.
Work sideways and vertical separately, join them with time, and ignore mass.
2 · Watch
Take it off screen
Where it sits
Where this leads
Jobs that lean on this skill. Follow one to see everything it is built on.
8 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.