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8.2MechanicsStretch

Vector Methods with Projectiles

Projectile motion can be handled neatly with vectors. The acceleration is the constant gravity vector −gj, and the suvat vector equations give position and velocity at any time.

24 min Video by Zeeshan Zamurred Further Kinematics
Edexcel A Level Maths: 8.2 Vector Methods with ProjectilesWatch the full walkthrough before the notes below.
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What you'll be able to do

  • Use a = −gj for projectiles
  • Apply vector suvat to projectile motion
  • Find velocity and position vectors
  • Determine when conditions are met
1

Gravity as a vector

For a projectile, the acceleration is (taking up as positive ). The velocity and position then follow from the vector suvat equations.

Gravity acts in the −j direction.
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2.
Answer

Tip — The i component of velocity stays constant; only the j component changes (by −gt).

Formula recap

Gravity vector.
Position vector.

Common mistakes to avoid

Applying gravity to the i component.
Gravity is in the −j direction only.
Forgetting the sign of g.
With up positive, the acceleration is −gj.

Key takeaways

  • Projectile acceleration is a = −gj.
  • Use vector suvat for velocity and position.
  • The i (horizontal) component is unchanged.

Test yourself

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