6.1MechanicsCore

Horizontal Projection

A projectile launched horizontally has independent horizontal and vertical motions. The horizontal velocity is constant; the vertical motion is free fall under gravity. Treating them separately is the key idea.

24 min Projectiles

Edexcel A Level Maths: 6.1 Projectiles (Horizontal Projection)Curated by Kepler, not produced by us. Watch it before the notes below.

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What you'll be able to do

Separate horizontal and vertical motion
Use constant horizontal velocity
Apply suvat vertically with a = g
Find time of flight and range

Two independent motions

Horizontally there is no acceleration, so $x = ut$ . Vertically the object falls under gravity from rest (in the vertical direction), so $y = \tfrac12 g t^2$ downward. Time links the two.

x = ut, \qquad y = \tfrac12 g t^2

Horizontal constant speed; vertical free fall.

Example 1A ball is thrown horizontally at 10 m/s from a 20 m cliff. Find the time to land (g = 9.8).

1Vertical:

20 = \tfrac12(9.8)t^2

t^2 = \tfrac{40}{9.8} \Rightarrow t \approx 2.02

Answer

t \approx 2.02

Tip — Time of flight is found from the VERTICAL motion, then used in the horizontal equation.

Formula recap

x = ut

Horizontal (constant speed).

y = \tfrac12 g t^2

Vertical (from rest).

Common mistakes to avoid

Applying gravity to the horizontal motion.

Horizontal velocity is constant; gravity acts only vertically.

Finding range without first finding the time.

Get time from the vertical motion, then x = ut.

Key takeaways

Horizontal and vertical motions are independent.
x = ut horizontally; y = ½gt² vertically.
Find the time from the vertical drop first.

Test yourself

Answer a few questions, then review anything you missed.

Prefer paper? Open the written self-check

Answer each question before opening its answer. This self-check does not record a quiz score.

In projectile motion, the horizontal velocity is:
- constant
- increasing
- decreasing
- zero
Show answer and explanation
Answer: constant
No horizontal force.
The vertical motion has acceleration:
- $g$ downward
- $0$
- $g$ upward
- constant velocity
Show answer and explanation
Answer: $g$ downward
Gravity.
Horizontal distance is given by:
- $x = ut$
- $x = \tfrac12 g t^2$
- $x = ut + \tfrac12 g t^2$
- $x = u$
Show answer and explanation
Answer: $x = ut$
Constant speed.
A ball thrown horizontally off a 20 m cliff lands after (g=9.8):
- $\approx 2.02$ s
- $1$ s
- $4$ s
- $20$ s
Show answer and explanation
Answer: $\approx 2.02$ s
√(40/9.8).
To find the range you first find the:
- time of flight
- mass
- angle
- friction
Show answer and explanation
Answer: time of flight
From vertical motion.

Next step

Keep practising

Start with the quiz above to check the key ideas. You can also choose another topic from the practice library.

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Related lessons

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Put the methods into practice: see how A-Level maths duels work. An account is required to play; the overview and sample are public.