# A-level Mathematics/Edexcel/Mechanics 2/Particle Kinematics

## Kinematics of a particle moving in a straight line or plane

### Projectiles

Projectiles are objects, like cannonballs, that move freely under gravity along a curved. When dealing with projectiles in M2 we make a number of assumptions:

• There is no force acting horizontally on the particle (such as air-resistance).
• The only force acting vertically on the particle is gravity.

The key to understanding projectiles is to consider the particle in two dimensions, let's call them x and y. The in the x direction, the particles motion is unchanged (because there is no air resistance) and in the y direction, the particle is accelerating due to gravity. For example, a penny which is thrown horizontally from the top of a building will continue to move away from the building as it falls (horizontal motion does not stop as the velocity of the coin increases, it just becomes less noticeable).

The hardest part of most questions involving projectiles is resolving the particle's velocity into the x and y plane. For any angle at which a particle is projected the horizontal component is given by $V \cos{\theta}$ and the vertical is given by $V \sin{\theta}$. This makes sense, as if you have a particle projected at 90° to the horizontal, then the vertical component is given by $V \sin{90}$ (which is simply V) and the horizontal component by $V \cos{\theta}$ - or 0. Similarly if our particle is projected at 0°, then our horizontal is V and our vertical is 0.

Once the particle is in motion, you can solve equations separately on the x and y directions. So for example you could use the equation $v = u + at$ to work out how fast the particle is travelling vertically after it hits a wall 5 metres away.