## Equations for Projectiles

A Level Physics Notes: Forces and Motion - Equations for Projectiles

A projectile is a body that falls freely under gravity ie the only force acting on it is gravity. In fact this is never strictly true, since there is always air resistance for example, but these other forces are small compared to gravity in most circumstances so we ignore them.

We can resolve the initial velocity of the ball vertically and horizontally as shown:    (1)

The horizontal velocity is constant since there are no horizontal forces acting – gravity acts vertically. Horizontally therefore Vertically however, the particle is accelerating downwards. We usually take this acceleration as negative and equal to Vertically, we can apply all the normal suvat equations: We get, (2) (3) (4) becomes which we have already.

We can also derive an equation between and by rearranging (1) to give and substituting this into (3):  (5)

We can find the maximum height using with obtaining We can find the range by substituting in (5) to get Since the maximum range is given by when 