# Reference Frames and Shooting Flames

Posted on Wednesday, February 7th, 2024

Written by Colton Bourque

The story of two Toronto teens exploded in May 2023 after videos of them shooting fireworks on the bus caught fire. This seems to be a hot trend, as in just over a week there were seven incidents of fireworks on Toronto public transit (Casaletto, 2023). This eruption of firework usage in motorized vehicles has sparked the question: How do these blazing bullets fly and what changes when they’re triggered on a moving vehicle?

We first need to start with how fireworks fly, from the ground up. For our purposes, we can ignore air resistance and any changes in mass, which you will thank me for later! This leaves us with only two forces to worry about, the thrust that sends these missiles up to the heavens and the gravity that brings them back down to earth. If the firework is shot straight upwards, thrust and gravity play an airborne tug of war. Most decent fireworks will be able to outmuscle gravity for long enough to climb up into the sky, but gravity will eventually win and pull it back down to where it started. Things change significantly when you shoot fireworks forward instead of up, as the two forces are perpendicular then. This means that both forces are free to act independently, and neither slows the other down (until you run into the ground or a wall). Typically, gravity will pull the firework down to the ground pretty quickly, so aiming somewhere between these two extremes will leave you with enough hang time and displacement to not have it blow up in your face.

We now have a handle on how fireworks function in a still reference frame, so it’s time to explore how that can change once we’re in motion. A reference frame is a set of coordinates that we use to describe the relative motion between objects (DiSalle, 2020). A reference frame is also something that we get to choose; if we want to measure how fast a car is going, we would do it relative to the road to make our life easy (rather than doing it relative to the moon). Reference frames are super important because we can’t feel constant velocity; imagine trying to judge the speed of a car with your eyes closed. Unless we look out the window to see how fast we are going relative to another object, we would have no idea how fast we’re driving. Let’s take a look at some different reference frames we could use to observe a firework being shot off the bus in Figure 3.

Here we can see three different observers viewing the fireworks being shot upwards from the bus. To the observer on the bus, it goes up and down exactly as it did when it was shot off on still ground because the bus is moving at constant velocity. To the observer on the ground, the firework follows the bus as it drives away, giving it a parabolic shape. The car driver views a similar path as the pedestrian, but the parabola is much wider. We see this because the difference in velocity, often called the relative velocity, between the bus and the car is greater than that between the bus and the person standing still.

Now that we’ve learned all about reference frames, it’s time to use our knowledge for good. An evil public transit rider decides to shoot a firework off the bus and at your three friends, Jerry, Barry, and Garry (as seen in Figure 5). The firework is pointing perpendicular to the bus, and it starts its flight pointing directly at Barry. The catch is that none of your friends are looking, so somebody is getting a face full of flames unless you can tell the right person to duck. Using everything that we now know about reference frames, who do you think should duck?

If you said that Barry or Jerry should duck, then unfortunately Garry is going to be quite crispy. From the frame of reference of the ground, the fireworks will keep travelling with the bus and land ahead of where it was aimed. For the sake of Garry’s modelling career, please use your knowledge of reference frames and a little bit of common sense to be safe next time you use fireworks!

References

1. Casaletto, L. (n.d.). “Irresponsible behaviour”: TTC investigating after firework set off on bus. CityNews. https://toronto.citynews.ca/2023/05/30/ttc-investigating-after-fireworks-set-off-on-bus/
2. DiSalle, R. (2020, April 15). Space and time: Inertial frames. Stanford Encyclopedia of Philosophy. https://plato.stanford.edu/entries/spacetime-iframes/

Colton Bourque, an undergraduate student at the University of Guelph, produced this article in the context of the 3rd-year course IPS3000 on Science Communication in the Fall 2023 semester (course instructor: Alex Gezerlis, TA: Carley Miki).