A particle moving in a vertical plane under the action of gravity is known as a projectile.

Horizontal projection



The horizontal motion of a projectile is modelled as having constant velocity (\(a = 0\)).
The forumla \(s = vt\) can be used.

The vertical motion of a projectile is modelled as having constant acceleration due to gravity (\(a = g\)).
The \(suvat\) equations can be used.

Unless otherwise stated, use \(g\) = 9.8 ms^-2.

Projection at an angle



A particle is projected with initial velocity U at an angle α above the horizontal.

The velocity can be resolved into horizontal and vertical components:



\(\cos{α} = \dfrac{u_x}{U} \implies u_x = U\cos{α} \)

\(\sin{α} = \dfrac{u_y}{U} \implies u_y = U\sin{α} \)

The horizontal component of the initial velocity is \(U\cos{α}\).

The vertical component of the initial velocity is \(U\sin{α}\).

A projectile reaches its maximum height when the vertical component of its velocity is equal to 0.