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Gravity is the simplest force in nature to model and yet one of the richest sources of A-Level problems. Near the surface of the Earth, any object in free fall experiences a constant downward acceleration of magnitude g ≈ 9.81 m s⁻², regardless of its mass. This is the cornerstone of Galileo's famous result that, in the absence of air resistance, a feather and a cannonball fall side by side.
In this lesson, which covers OCR Module 3.1.3 (Projectile Motion), we apply the SUVAT equations to vertical free fall and then to two-dimensional projectile motion. The crucial insight is that horizontal and vertical motion are independent: they share the same clock but nothing else.
An object is in free fall if the only force acting on it is its own weight. On Earth, this means:
Under free fall, the acceleration of any mass is the gravitational field strength, g, measured in m s⁻² or equivalently N kg⁻¹. At the UK, g ≈ 9.81 m s⁻². At the equator it is slightly smaller (≈ 9.78), at the poles slightly larger (≈ 9.83), and on the Moon only 1.62 m s⁻².
Exam Tip: OCR expects you to take g = 9.81 m s⁻² unless the question states otherwise. Do not use 10 m s⁻² unless the paper explicitly uses it.
Newton's second law gives F = ma. For a freely falling body the only force is gravity, F = mg, so:
ma = mg ⇒ a = g
The mass m cancels. Every object experiences the same acceleration regardless of mass — provided air resistance is negligible. Apollo 15 astronaut David Scott famously demonstrated this on the Moon in 1971 by dropping a hammer and a feather simultaneously; in the airless lunar environment they hit the surface together.
A stone is dropped from a cliff. Ignoring air resistance, find (a) its speed after 2.5 s and (b) how far it has fallen in that time.
Take downwards positive, u = 0, a = 9.81 m s⁻², t = 2.5 s.
(a) v = u + at = 0 + 9.81 × 2.5 = 24.5 m s⁻¹
(b) s = ut + ½at² = 0 + ½ × 9.81 × 6.25 = 30.7 m
A ball is thrown vertically upwards at 20 m s⁻¹. Take upwards positive, a = −9.81 m s⁻².
Time to maximum height (v = 0):
Maximum height (v = 0):
Total time of flight (returns to starting height, s = 0):
Notice that the time up (2.04 s) equals the time down (4.08 − 2.04 = 2.04 s). This symmetry of free fall is a powerful shortcut: in the absence of air resistance, the time to rise equals the time to fall, and the speed at any height on the way up equals the speed at the same height on the way down.
OCR's PAG (Practical Activity Group) 1 includes measuring g using free fall. The most common method uses an electromagnet to release a steel ball and a light gate (or trapdoor switch) to time its fall through a distance h.
From s = ut + ½at² with u = 0:
h = ½ g t² ⇒ g = 2h / t²
By plotting h against t², the gradient is g/2 and thus g = 2 × gradient. A typical result gives 9.8 ± 0.1 m s⁻².
Sources of error:
A projectile is an object launched with an initial velocity and moving thereafter under gravity alone. Examples: a cricket ball, a shell, a skier leaving a ramp.
The key physical insight, first recognised by Galileo, is:
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