6.2MechanicsStretch

Horizontal and Vertical Components

When a projectile is launched at an angle, its initial velocity splits into horizontal and vertical components. These components then evolve independently — horizontal constant, vertical changing under gravity.

24 min Video by Zeeshan Zamurred Projectiles

Edexcel A Level Maths: 6.2 Projectiles (Horizontal and Vertical Components)Watch the full walkthrough before the notes below.

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What you'll be able to do

Resolve the launch velocity into components
Use u cos θ and u sin θ
Track each component over time
Find velocity at a later instant

Initial components

A speed $u$ at angle $θ$ has horizontal component $u cos θ$ (constant) and vertical component $u sin θ$ (decreasing under gravity, then increasing downward).

u_{x} = u cos θ, u_{y} = u sin θ

Resolving the launch velocity.

1Horizontal:

25 cos 40° \approx 19.2

m/s.

2Vertical:

25 sin 40° \approx 16.1

m/s.

AnswerH ≈ 19.2 m/s, V ≈ 16.1 m/s.

Tip — The horizontal component stays the same throughout the flight.

Velocity later on

The horizontal component is unchanged; the vertical component changes by $- g t$ (taking up as positive). Combine them to get the speed and direction at any time.

Formula recap

u_{x} = u cos θ

Horizontal (constant).

v_{y} = u sin θ - g t

Vertical (changes with time).

Common mistakes to avoid

Letting the horizontal component change with time.

Only the vertical component changes (under gravity).

Swapping cos and sin for the components.

Horizontal uses cos θ; vertical uses sin θ.

Key takeaways

Resolve: uₓ = u cos θ, u_y = u sin θ.
Horizontal component is constant.
Vertical component changes by −gt.

Test yourself

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