Author: Ali Mohammed Redha, King Abdullah University of Science and Technology, Saudi Arabia
Overthinking a Simple Question
Figure 1: Showing a famous post popularized by World of Engineering social media accounts asking: “which of these trucks are driving?” [1]
1 Motivation
You have probably come across this post (Figure 1) somewhere on social media. It is a famous “trick question” that is meant to stir up discussions, of which there are many. I came by this post numerous times, often going to read the comments, be amused by how many incorrect answers to the question, and then moving on. Being a physicist, I knew the answer and it was as clear as it can be. Having such a question answered incorrectly most of the time was not a big deal, as the question is meant for fun.
Recently, I came across the post again on Instagram, this time as part of a Ramadan daily quiz made by an academy that I am part of. I waited anticipatingly for the results to be announced. The answer was announced, and it was “C”. “Hmm…Surely they are not serious”, I thought. An attempt by multiple participants was made to clarify the correct answer, but the organizers insisted on the answer. In the end, the clarification attempts failed, and the answer remained “C”.
Although it has been a while now since that incident, I still have it roaming around my head. “The question is simple. How could they have gotten it so obviously wrong?” Thus, I decided to dig deeper into the problem, hoping to find an answer.
2 What Exactly Does the Question Want?
When a physicist thinks about a problem, they immediately start thinking about the exact meaning behind the question. Here, we want to know which of these trucks are moving in the indicated direction.
Based on your background, this is either “very easy” or “impossible”. The obvious answer is “A” is moving backward, “B” is stationary, and “C” is moving forwards. Problem solved right? Not quite. There are more details underneath this problem than what is immediately thought. Let us take into consideration all the different cases instead of talking about the problem abstractly. Consider this thought experiment.
Imagine you are in a car and the car is stationary. Suddenly, the car starts accelerating fast reaching 100 km/h in 5 seconds, what will happen to you? You will feel a strong pushback due to inertia, almost clinging you to your seat. This is similar to the case “C” in the question. Imagine afterward the car stays moving steadily at 100 km/h for a while. Then, all of a sudden, the brakes are hit, and the car decelerates to 20 km/h in 5 seconds, what will happen to you? You will feel a push also caused by your inertia, but this time it will push you forward. Think about it, the car was still moving forward, yet you felt a push forward. This is like case “A”. We have shown that both cases “A” and “C” are possible to be moving in the forward direction.
Even case “B” is possible to be moving forward. Imagine if the car brakes are not hit, and the car keeps moving at 100 km/h for a long time. What will happen? You will stay still as if you are not even moving. As you can see, all of the cases are possible to be moving in the direction stated in the problem. Except there is more to it than just this.
Consider now that everything is reversed. The stationary car, with you in it, starts moving backward reaching 100 km/h in reverse. What will happen to you now? You will feel a push forward (opposite the direction of motion). If the car then stays moving at that speed for a while, you will feel as if you are stationary. And again, when the car decelerates from 100 km/h to 20 km/h, you will feel a push backward (with the direction of motion). This means that all the cases are possible to be moving in the opposite direction as well!
It can get even more counterintuitive, as one can make an argument that they all can be stationary, and it would be true in certain circumstances. For a physicist, this should not be surprising, as physics tells us everything we need to know about these answers.
3 The Physics Behind It
In physics, motion means the change of position in the direction specified and that has a name. We call it velocity. So, to answer the question, we need to know the direction of the velocity of each truck. However, the three images given do not give any indication whatsoever about the direction of the velocity. Instead, it gives us the direction of the force applied to the liquid, or in other words, the direction of the acceleration.
According to Newton’s first law, a stationary object would stay stationary, and a moving object would stay moving at constant speed unless a net force acts upon it [3]. This in a way, is the case “B”. A moving object with constant speed cannot distinguish (physically) whether it is moving or not. This is known as the principle of relativity (first made famous by Galileo Galilei) [2]. This means that we cannot physically sense speed (by touch at least). Newton’s second law gives us what an applied force does, and that causes acceleration [3]. Acceleration is the change of motion (velocity). A change backward would give us the answer “A” and a change forward would give us the answer “C”, due to the famous phenomena of inertia. See, this does not tell us in any way what is the direction of velocity. The directions of the velocity and acceleration are independent of each other. So, in each of the three cases, the object can be moving in any direction. As a matter of fact, it can even be moving sideways, vertically, or even at an angle!
If you go back to the post, the answers with the most likes are those saying all choices are possible [1]. In fact, some say that the wording of the question supports this answer (“are” not “is”). However, some other comments come up with a good counterpoint. The question says “driving” and generally, driving is done by hitting the gas pedal, not the brakes! Therefore, the answer is “C”. Maybe this is what the organizers meant in that answer? To that I say, yes you got a point. But I would still argue that the answer is not just “C”, not just from the previous argument (as the car still can decelerate even with pushing the gas pedal), but also for another entirely different one. Let me show you why.
4 Overthinking the Question
For those observant, there is a slight flaw in our theoretical experiment. We used a solid object – you dear reader – as a replacement for the liquid in the problem. And this is a technical issue in the experiment, as liquids behave differently than solids.
Liquids, unlike solids, do not have a fixed shape. And so, a force acting on a liquid would produce vastly different results than a force acting on a solid. A rigid solid object would remain intact upon a simple touch, and a liquid, like water would start vibrating, with waves rippling on its surface. That is just a simple touch of the hand. A strong force would cause a larger vibration on the water’s surface and would cause its shape to deform significantly.
Now apply this to the case we have. The truck is stationary with all the liquid on it, then it starts accelerating strongly forward abruptly. The liquid will be pushed backward at first, but upon hitting the back of the container will start waving back and forth. What we will get is chaos, in the logical and physical sense. The motion of liquids in such cases is chaotic, similar to tossing a coin or using random.org [4]. Hence, case “C” would not be replicated precisely during a forward acceleration of the truck. If you take 1000 images of the truck accelerating forward, maybe you will be able to replicate image “C”, except do not hedge your chances of having it stay constantly the same. Fun fact, you might be able to get images of “B” or even “A” if you were lucky enough! Things need to go a specific way, but it is possible! Thus, you might be able to get images “A”, “B” and “C” in the same “photo shoot”. Even with the notion that hitting the brakes is not driving, we still got all the images which means all of the answers are possible. Let us take one more thought experiment to explore another possibility.
5 Overthinking It to Absurdity
Imagine the truck with the fluid inside it, and we take that truck and shake it violently. After that, we let it rest in a pure isolating chamber, where it cannot interact with anything at all. During this time, we took our special x-ray camera and took a large number of photos (theoretically an infinitely large number of them). If we then filter out these photos, we will see the three cases among them. The point is that the force applied on the truck does not have to be by the truck (engine) itself. It can be caused by other means.
The complexity of the problem does not stop there. I mentioned previously that the reaction of liquids to forces is chaotic, meaning it depends on many factors. These factors include, but are not limited to: the type of liquid (determining its density, viscosity, etc.), the volume and temperature of the liquid, the material the container is made of, the type of gas (if any) with the liquid inside the container and its temperature, ambient air temperature, wind currents, amount of sun radiation incident, the surface of the road and the tiers, vibrations caused by the car engine and motors, and the remaining is left for the reader to figure out as an exercise [5]. This adds layers upon layers to the already, too complicated simple problem .
6 Conclusion
The final answer to this question is: all and none of the above (this is a first!). This problem highlights one trick of mother nature. How our senses fool us and build our intuition on a physically incorrect notion. This is why we have to be careful when dealing with physics, as more often than not, physics can be counterintuitive (which in and of itself is counterintuitive). Ultimately, the answer to this question does not matter. It is for fun. What matters is how people perceive this problem. Everyone is going to understand it in their unique way, which opens the floor for some great discussions. It is astonishing to come across a question occasionally where there can be no winner or loser. Just different perspectives on a fascinating, tricky problem. In such a scenario, the true winner is everyone who got enlightened by a nice, eye-opening discussion. Not everything has to be a competition after all… and yes, I did write this to prove a point.
7 References
[1] World of Engineering. Which of these trucks are driving?: https://twitter.com/engineers_feed/status/1592207414367252480 2022 Nov 14 [cited 2023 April 27] [Tweet]. Available from: @engineers_feed.
[2] Wikipedia contributors. Principle of relativity [Internet]. Wikipedia, The Free Encyclopedia; 2023 Mar 27, 20:46 UTC [cited 2023 Apr 27]. Available from: https://en.wikipedia.org/wiki/Principle_of_relativity.
[3] Glenn Research Center. Newton’s Laws of Motion [Internet]. Glenn Research Center – NASA. [Cited 2023 May 21]. Available from: https://www1.grc.nasa.gov/beginners-guide-to-aeronautics/newtons-laws-of-motion/
[4] Bishop R. Chaos. The Stanford Encyclopedia of Philosophy; 2017 Mar 21 [cited 2023 May 21]. Available from: https://plato.stanford.edu/entries/chaos/
[5] Wikipedia contributors. Fluid dynamics [Internet]. Wikipedia, The Free Encyclopedia; 2023 May 4, 18:13 UTC [cited 2023 May 21]. Available from: https://en.wikipedia.org/wiki/Principle_of_relativity.