Form 4 · Chapter 2

Free Falling

A freely falling object moves under gravity alone, accelerating downward at g ≈ 9.81 m s⁻² regardless of its mass.

What is free fall?

An object is in free fall when the only force acting on it is gravity, with air resistance ignored. Every freely falling object has the same acceleration, the gravitational acceleration g ≈ 9.81 m s⁻² (often taken as 10 m s⁻² in calculations), directed downward. Mass does not affect this — a feather and a coin fall together in a vacuum.

Key formula

Use the equations of motion with a = g:
v = u + gt
h = ut + ½gt²
v² = u² + 2gh
Take downward as positive; for a dropped object u = 0.

Dropped from rest

If an object is simply dropped, u = 0, so v = gt and h = ½gt². The speed increases by about 10 m s⁻¹ every second (using g = 10 m s⁻²).

Worked example

A ball is dropped from a height and falls for 3 s. Using g = 10 m s⁻², find its final velocity and the height fallen.
v = u + gt = 0 + (10)(3) = 30 m s⁻¹.
h = ut + ½gt² = 0 + ½(10)(3²) = ½ × 10 × 9 = 45 m.

Thrown upward

An object thrown up decelerates at g, stops momentarily at the top (v = 0), then falls back. At maximum height v = 0.

Remember

  • All objects fall with the same g when air resistance is ignored.
  • For a dropped object u = 0.
  • At the highest point of upward motion, v = 0.

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