Projectiles

This lesson covers projectile motion at A-Level, where objects move in two dimensions under the influence of gravity alone. The key principle is that horizontal and vertical components of motion are treated independently.

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Assumptions in the Projectile Model

The standard projectile model assumes:

• The object is a particle (no air resistance, no spin).
• The only force acting is gravity (vertically downwards, $g = 9.8$g=9.8 m/s$^2$2).
• Horizontal velocity is constant (no horizontal forces).
• Vertical motion has constant acceleration $g$g downwards.

Exam Tip: If asked to "state assumptions", always mention: the object is modelled as a particle, air resistance is neglected, and $g$g is constant. You should also note that the ground is assumed to be flat and horizontal.

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Resolving Initial Velocity

If an object is projected at speed $U$U at angle $\theta$θ above the horizontal:

Component	Value
Horizontal	$U_x = U\cos\theta$Ux​=Ucosθ
Vertical	$U_y = U\sin\theta$Uy​=Usinθ

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Equations of Motion

Horizontal Motion (constant velocity)

$x = U\cos\theta \cdot t$x=Ucosθ⋅t

There is no horizontal acceleration, so horizontal velocity remains $U\cos\theta$Ucosθ throughout.

Vertical Motion (constant acceleration $-g$−g)