Spark image

Projectiles and air resistance

Objects moving through air are slowed down due to air resistance, sometimes called drag. This air resistance affects a spacecraft when it re-enters the Earth's atmosphere but also the path of a projectile such as a bullet or a ball. When air resistance is taken into account the trajectory of a projectile is changed. The resistance is often taken as being proportional to either the velocity of the object or the square of the velocity of the object.

The medieval scientists believed that a projectile went upwards at an angle along a straight path, then went through a short curved section before falling vertically back to the ground again.

Both the range of a projectile and the maximum height that it reaches are affected by air resistance. The mathematics of the motion is quite complicated (especially if you consider the change in the shape and/or surface of a projectile and the variation of the density of the air with height) but the following diagrams try to simplify things by showing generally how air resistance affects both the trajectory and the velocity of a projectile.

The blue lines show the projectile with no air resistance and the red lines show what happens when air resistance is taken into account. The maximum height, the range and the velocity of the projectile are all reduced.

A useful website with an interactive applet is: Air resistance

© Keith Gibbs 2020