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 (OCR A Level Maths: Mechanics)

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. Mechanics Toolkit

1.1 Quantities, Units & Modelling

1.1.1 Scalars & Vectors

1.1.2 Fundamental Units

1.1.3 Derived Units

1.1.4 Types of Force

1.1.5 Modelling Assumptions

1.2 Working with Vectors

1.2.1 Working with Vectors

2. Kinematics

2.1 Kinematics Graphs

2.1.1 Displacement-Time Graphs

2.1.2 Velocity-Time Graphs

2.1.3 Drawing Travel Graphs

2.2 Variable Acceleration - 1D

2.2.1 Using Calculus in 1D

2.3 Constant Acceleration - 1D

2.3.1 Deriving the suvat Equations

2.3.2 suvat in 1D

2.3.3 Acceleration due to Gravity

2.4 Variable Acceleration - 2D

2.4.1 Using Calculus in 2D

2.5 Constant Acceleration - 2D

2.5.1 suvat in 2D

2.6 Projectiles

2.6.1 Horizontal & Vertical Components

2.6.2 Using suvat

2.6.3 Equation of a Trajectory

2.6.4 Deriving Projectile Formulae

3. Forces & Newton's Laws

3.1 Forces

3.1.1 Force Diagrams

3.1.2 Equilibrium in 1D

3.1.3 Equilibrium in 2D

3.1.4 Forces in 2D - Vector Notation

3.2 Newton's Second Law

3.2.1 F = ma

3.2.2 Connected Bodies - Ropes & Tow Bars

3.2.3 Connected Bodies - The Lift Problem

3.2.4 Connected Bodies - Pulleys

3.2.5 F = ma - Vector Notation

3.3 Further Forces & Newton's Laws

3.3.1 Resolving Forces & Inclined Planes

3.3.2 Coefficient of Friction

3.3.3 Coefficient of Friction - F = ma

3.3.4 Coefficient of Friction - Inclined Planes

3.3.5 Coefficient of Friction - Harder Problems

4. Moments

4.1 Moments

4.1.1 Moments Diagrams

4.1.2 Using Moments - Equilibrium

4.1.3 Centres of Mass

4.1.4 Tilting

4.1.5 Using Moments - Harder

Author: Dan