1.3.4 Deriving Projectile Formulae

Deriving Projectile Formulae

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

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

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.