Projectile Motion

This lesson covers projectile motion as required by the Edexcel 9MA0 A-Level Mathematics specification. A projectile moves in two dimensions under gravity alone — this combines horizontal constant velocity with vertical constant acceleration.

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Assumptions

The standard projectile model assumes:

• The projectile is a particle (no air resistance, no spin).
• Acceleration due to gravity, g, acts vertically downwards and is constant (9.8 m s⁻²).
• The horizontal acceleration is zero — there is no air resistance.

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Resolving the Initial Velocity

If a projectile is launched with speed u at angle θ above the horizontal:

• Horizontal component: ux = u cos θ
• Vertical component: uy = u sin θ

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Equations of Motion

Horizontal (no acceleration)

x = (u cos θ)t

Vertical (constant acceleration g downwards)

Taking upwards as positive:

vy = u sin θ - gt y = (u sin θ)t - ½gt² vy² = (u sin θ)² - 2gy

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Key Results

Time of Flight

The total time for the projectile to return to its launch height (y = 0):