Let’s Get Physics-l: Projectile Motion

Before we deal with the curve ball that is projectile motion, let us first contemplate simple vertical motion. Picture yourself throwing an object up and down (Be it a tennis ball, small child or the severed head of your arch nemesis. You know what, stick with a tennis ball). Assuming you throw it straight up, you should observe the ball rise up and then fall back down. As it rises, its speed decreases due to the force of gravity pulling it down. We can use the value of g here to calculate speed at different points but, in this instance, it is a negative value as the ball is working against gravity. The ball will eventually reach a maximum displacement (Maximum distance from you) where it stops momentarily, it’s velocity now nought. Gravity then pulls the ball back down to Earth, the ball now speeding up as it works with gravity. This sort of motion is far less weird than what follows.

Again, I’m going to delay it a little longer. Picture the scene. The Superhero Civil War has peaked at an airport in Germany. Hawkeye and Black Panther are currently engaged in a face off (Hawkeye clearly isn’t well read on food chains. Birds are known prey of Cats… What was he thinking!) Hawkeye draws back an arrow and launches it Black Panther. However, Black Panther catches the arrow and proceeds to attack Hawkeye. Silly Hawkeye.

IMG_4090.JPGAs fun as that scene is, what we are looking at is the arrow fired by Hawkeye. If you look above, The arrow follows what would be a symmetrical flight path (My artistic skills leave much to be desired). Calculating stuff from the arrows flight path is tricky, I won’t lie, but far from impossible. First things first, we have to break it down into it horizontal and vertical components.


Vv represents the vertical component of the arrow whilst Vh is the horizontal component. V is the all important component we can use to calculate the other two. One extra detail I forgot to include (Two mistakes in one day, what is going on!) is the angle X. X is the angle between the horizontal component and V. With this we can calculate the other two components using trigonometry (Please hold back grunts of distain, it has to be done I’m afraid).

To calculate each respective component we use:

  • Vv = VsinX
  • Vh = VcosX

It’s not that bad, really.

Another important point to mention is the nature of these components. If we ignore air resistance, the Horizontal component remains constant through out the entire flight. This is really helpful for calculations later on. The Vertical component is slightly more complicated. Remember how with vertical motion the tennis ball slowed down as it went up and sped up as it fell back down? Well, projectile motion is very much the same. As an object rises to its maximum displacement above the ground, it slows down as it is working against gravity. As it returns back to the ground, it speeds up, working with gravity.

As you can see, the vertical component decreases as the arrow rises but increases as the arrow falls. The horizontal component remains constant throughout.

Let’s put this into practice with a worked example:

Worked Example.png


  • Vertical motion
    • Up – negative g
    • Peak – momentarily at rest
    • Down – positive g
  • Projectile Motion
    • Horizontal Component
      • VcosX
      • Constant
    • Vertical Component
      • VsinX
      • Decreases up, increases down
    • SUVAT Equations: What to remember
      • Vertical speed at peak = 0m/s
      • Time to reach peak = 1/2 total time

Projectile motion, ladies and gentlemen. I hope this has been somewhat informative but if you do have any questions please leave them in the comments and I will do my best to provide an answer. Please also feel free to share your thoughts or feedback in the comments below. Thank you.


No small tree people, pink aliens, archers or people who dress in cat costumes were harmed in the making of these posts.


(The Characters referenced are property of Marvel comics and I in no way lay claim to them. They have simply been used to help better convey a physics concept).


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