One of the things we spoke about today was the difficulty of dealing with horizontal and vertical velocities one at a time when we analyse the motion of a projectile. I have uploaded this diagram to see if it will help you see how the horizontal and vertical velocities change as we look at different parts of the trajectory. You can click on the diagram to see a larger version if you like.

Hopefully you can see the arrow I have drawn in for the velocity of the projectile at any point – it’s the brown arrow. I have added blue and green arrows to this.

The **green** arrows show the horizontal motion of the projectile. The **green** arrows stay the same length throughout the flight because there is no unbalanced force acting in this direction (Newton’s 1st Law told us that balanced forces result in a constant speed).

Looking again at the diagram, you should notice that the **blue** arrows show the vertical velocity of the projectile. The **blue** arrows change as we move along the trajectory. For the first half of the diagram, the **blue** arrows point up because the projectile continues upwards towards it maximum height (called the **apex**). As the projectile travels towards the apex, gravity acts to slow it down – *we have deceleration due to gravit*y. This is why the **blue** arrows get shorter – the **length of the arrow** shows the **size** or **magnitude** of the velocity. Once it has passed the apex, the projectile falls downwards. The diagram shows that the **blue** arrows point **downwards** during the second half of the journey. As the projectile **falls**, it’s **vertical velocity increases** (it is speeding up) and this is shown by the **blue** arrows getting longer. *This is acceleration due to gravity*.

Notice that all the time that the **blue** arrows change their length and direction, the **green** arrows always have the same length and point in the same direction. **Horizontal velocity is constant in projectile motion**.

We can analyse **horizontal** motion quite easily using the relationship between speed, distance and time.

To analyse the **vertical** motion, we need to use the equations of motion.