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 Video by Zeeshan Zamurred Projectiles

Edexcel A Level Maths: 6.1 Projectiles (Horizontal Projection)Watch the full walkthrough 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 $x = u t$ . Vertically the object falls under gravity from rest (in the vertical direction), so $y = \frac{1}{2} g t^{2}$ downward. Time links the two.

x = u t, y = \frac{1}{2} g t^{2}

Horizontal constant speed; vertical free fall.

1Vertical:

20 = \frac{1}{2} (9.8) t^{2}

t^{2} = \frac{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 = u t

Horizontal (constant speed).

y = \frac{1}{2} 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

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