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

Gravity as a vector

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

a = - g j, v = u - g t j

Gravity acts in the −j direction.

v = 7 i + 10 j - 9.8 j

= 7 i + 0.2 j

Answer

7 i + 0.2 j

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

Formula recap

a = - g j

Gravity vector.

r = u t - \frac{1}{2} g t^{2} j

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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