The big idea: A projectile is anything moving through the air with only gravity acting on it (a thrown ball, a kicked football).
Split its motion into two separate parts: sideways (horizontal) and up/down (vertical).
Sideways the velocity stays constant. Up/down it is free fall (speeds up at g = 9.8 m s⁻²). The two parts don't affect each other — they just share the same time.
[Diagram: phys-projectile] - Available in full study mode
Spot it: two columns: Always make two columns — horizontal and vertical — and fill each separately.
Horizontal: constant velocity (no acceleration). Vertical: free fall (a = g). The time is the same in both.
Because the two parts are independent, you use free-fall equations for the vertical part and a simple distance = speed × time for the horizontal part. The shared time of flight comes from the vertical drop.
Which equation goes in which column?: Vertical (free fall): use the given equations of motion with a = g.
Horizontal (constant velocity): the velocity never changes, so just range = horizontal velocity × time.
- vertical drop / height fallen (m)
- initial vertical velocity (m s⁻¹) — 0 if launched horizontally
- acceleration of free fall, 9.8 m s⁻² (given)
- time of flight (s)
- horizontal range / distance (m)
- horizontal velocity, stays constant (m s⁻¹)
- time of flight (s)
[Diagram: phys-formula-triangle] - Available in full study mode
IB-style question — horizontal launch off a cliff
A stone is thrown horizontally at 12 m s⁻¹ from a cliff 20 m high. Take g = 9.8 m s⁻². Find (a) the time to hit the ground, then (b) how far from the base of the cliff it lands.
Part (a) — time of flight (vertical column)
- Vertical part is free fall from rest (uy = 0). Start with the given formula:
- Put in the numbers (s = 20, uy = 0, g = 9.8):
- Rearrange for t and take the square root:
Final answer
time of flight = 2.0 s.
IB-style question — (b) how far it lands
Same stone (thrown horizontally at 12 m s⁻¹ from the 20 m cliff). Find the horizontal distance to where it lands.
Part (b) — range (horizontal column)
- Horizontal velocity is constant. Use the horizontal formula:
- Put in ux = 12 and the time t = 2.0 s from part (a):
- Work it out — keep the unit:
Final answer
it lands 24 m from the base of the cliff.
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How this is tested: Projectiles show up as a quick compare/identify question on Paper 1A and as a full calculation on Paper 2.
- Paper 1A: compare a ball launched horizontally with one dropped or thrown straight down from the same height. - Paper 2: find the time of flight, the range, or the impact speed/angle.
Classic trap: the horizontal velocity does not change the fall time. Two balls dropped from the same height hit the ground together, whether or not one is also moving sideways.
Same drop → same fall time: The fall time depends only on the vertical motion (the height and g).
The sideways velocity adds horizontal distance, but it does not make the ball fall any faster or slower.
[Diagram: phys-projectile] - Available in full study mode
IB-style question — dropped vs thrown horizontally
From the top of the same cliff, ball P is simply dropped and ball Q is thrown horizontally, both at the same instant. They start at the same height. Which lands first, and why?
Solution
- Fall time depends only on the vertical motion — the height and g.
- Both balls start with zero vertical velocity and fall the same height.
- Q's sideways velocity is horizontal — it adds distance but not vertical speed, so it does not change the fall time.
Final answer
They land at the same time. The horizontal launch only moves Q sideways; the drop (and so the fall time) is identical.