# Physics Explained Through a Video Game/Calculating Displacement

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## Topic 1.2 - Calculating Displacement

[edit | edit source]We can calculate for the exact displacement of an object in a particular direction by considering the final and initial positions of an object in that direction. Then, we subtract the initial position value from the final position value to get the change in position, which is displacement.

This allows for us to quantitatively look at the change in an object's position, which will later make it possible to make clearer predictions about objects in motion.

```
Formula for displacement in the X (horizontal) direction:
```

```
Formula for displacement in the Y (vertical) direction:
```

If we have a displacement that has both a vertical and a horizontal component, we can add these displacement vectors together to get the **net displacement**vector.

Question 1:Suppose that there's an in-game situation where the playerwants to knockHello(colored white)Jensen(colored grey)off the board. At a particular time in the game,Helloneeds to have a of and a of in order to reachJensen. How far doesHelloneed to travel in order to reachJensen, assuming thatJensenis at the same spot whenHelloarrives?

**Solution:**

*Hello*needs to travel, we need to find . Using the image on the right, we can see that if we were to draw from where ends, we form a right angle between these two displacement components. Also, we know that because the net displacement is the shortest path between two points, must be a line directly connecting

*Hello*to

*Jensen*.

Thus, we can form a right angle triangle that is outlined by and its components. Because of the Pythagorean Theorem where where a and b are components and c is , we can show that:

Note that any displacement can either be positive or negative, depending on what is convenient for the situation. In this case, because we are looking for the magnitude of distance between * Hello* and

*, we can allow for to be positive such that: (using 1 significant figure).*

**Jensen**- ↑ "Significant Figures".
*Science Olympiad Student Center*. April 3, 2014. Retrieved July 26, 2024.