Free Fall
Drop it, throw it up: gravity runs the same equations every time.
Lesson at a glanceShow the key points
- Near Earth, ignoring air resistance, all bodies fall with the same constant acceleration g ≈ 9.8 m/s² downward.
- With upward positive: v = u − gt, y = ut − ½gt², v² = u² − 2gy.
- A body thrown up at u rises for u/g seconds to a height u²/2g above the launch point.
- The motion is symmetric: it passes each height on the way down with the speed it had on the way up.
The most familiar constant acceleration of all is right under your feet. Drop anything, and gravity applies the same equations of motion every single time.
Falling is constant acceleration
Ignore air resistance and let go of an object near the Earth’s surface. It falls along a vertical straight line with an acceleration that points straight down and is very nearly constant, as long as the height involved is tiny compared with the Earth’s radius (about 6400 km). Its magnitude is about 9.8 m/s² (or 32 ft/s²), and it gets its own symbol, .
Because is constant, the three equations from the previous lesson apply directly. Only the signs need care, and they depend on which way you call positive.
In both, is the coordinate measured from the starting point (y = 0 at t = 0), is the initial velocity and the velocity at time t, each with the sign set by your chosen convention.
A ball is tossed straight up at 6.0 m/s. Taking g = 10 m/s², how high does it rise?
A stone is dropped (u = 0) from a 20 m roof. When does it land and how fast is it going? Use g = 10 m/s².
- 1Near Earth (no air resistance), everything falls with the same constant acceleration g ≈ 9.8 m/s² downward.
- 2Choose a positive direction and stick with it; g gets a minus sign if upward is positive.
- 3Maximum height above the launch point: ; time to get there: .
Check yourself
Keep exploring
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