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. The rule behind it is s = u t + 1/2 a t squared, so for a fall from rest, where u is 0 and a is g, it becomes s = 1/2 g t squared.
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.
More to read
3.4 Projectile Motion
A projectile flies two motions at once, and they ignore each other. Sideways it cruises at a steady speed because no force pushes it that way. Up and down it falls with the usual gravitational acceleration. Give each direction its own list of u, v, a, s and t, and link the lists through time alone. Split first, solve each half with plain 1D equations, then reunite at the end.
4.3 Projectile Motion
The two motions are independent. A ball rolled off a bench keeps its sideways speed all the way down while gravity builds its downward speed from zero. Time of fall comes from the vertical drop alone, then range is sideways speed times that time. Mass appears nowhere: heavier balls fall no faster and carry no extra sideways push. Predict the landing spot with a stopwatch and a ruler, not a scale.
5.3 Projectile Motion
Setting up the two lists cleanly prevents most mistakes. Write horizontal first: acceleration zero, velocity fixed, distance equals speed times time. Then vertical: acceleration g downward, initial velocity often zero for bench launches, distance from the drop height. Solve vertical for time, carry it across, and finish horizontal. When answers look odd, check signs first: down is usually negative if up was called positive.
Explore more
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.