Deriving Projectile Formulae

What projectile formulae do I need to be able to derive?

In the previous notes the equation of the trajectory of a particle was derived
Other equations you need to be able to derive are
- $time of flight (between launch and land) = \frac{2 U \sin θ}{g}$
- $the (horizontal) range of the projectile = \frac{U^{2} \sin 2 θ}{g}$
- $the time taken to reach the maximum height = \frac{U \sin θ}{g}$
- $the maximum height = \frac{U^{2} \sin^{2} θ}{2 g}$
These are derived using the suvat equations
Whilst you do not need to memorise every step of the derivations, you should concentrate of the methods used and know how to approach each one
There is no worked example with this revision note, instead see if you can use your knowledge of the suvat equations as well as geometrical and algebraic reasoning to derive the above equations before reading on

2-6-2-using-suvat-diagram-1

How do I derive the projectile formulae?

A particle is projected with speed U m s^-1 at an angle of θ° to the horizontal
All of the derivations assume that:
- the launching and landing site are at the same vertical level
- the projectile travels over horizontal ground
- there are no forces acting on the particle other than the force due to gravity

2.6.4 Deriving Projectile Formulae Diagram 1_1, downloadable Edexcel A Level Mechanics revision notes

2-6-4-deriving-projectile-formulae-diagram-2

Examiner Tip

Always draw a sketch!
The trickiest part about this is the algebra so do not rush these questions as that is when you are more likely to make mistakes.
Make sure you can follow the derivations above as they could be asked. After reading through this revision note practice replicating the derivations from memory.

Deriving Projectile Formulae (Edexcel International A Level Maths: Mechanics 2)

Revision Note

What projectile formulae do I need to be able to derive?

How do I derive the projectile formulae?

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1. Kinematics (Straight Line Motion)

1.1 Variable Acceleration - 1D

1.1.1 Using Calculus in 1D

1.2 Variable Acceleration - 2D

1.2.1 Using Calculus in 2D

1.3 Projectiles

1.3.1 Horizontal & Vertical Components

1.3.2 Using suvat

1.3.3 Equation of a Trajectory

1.3.4 Deriving Projectile Formulae

2. Centres of Mass

2.1 Centres of Mass

2.1.1 Particles

2.1.2 Uniform Laminas

2.1.3 Composite Laminas

2.1.4 Frameworks

2.1.5 Objects Suspended in Equilibrium

2.1.6 Point of Tipping

2.1.7 Non-unform Objects & Other Problems

3. Work and Energy

3.1 Work & Energy

3.1.1 Work

3.1.2 Energy

3.1.3 Energy Principles

3.2 Power

3.2.1 Power

4. Collisions

4.1 Collisions

4.1.1 Impulse in 2D

4.1.2 Collisions - Multiple Collisions

4.1.3 Coefficient of Restitution

5. Moments

5.1 Statics of Rigid Bodies

5.1.1 Using Moments - Harder

Author: Dan