A problem regarding Galilean relativity

• CherryWine
In summary, the problem states that two bodies are moving on the same line, with one moving away from the other and the other moving towards. The distance between them changes by 16m in 3 seconds for the first case and by 3m in 3 seconds for the second case. The respective speeds of the two bodies can be determined by using basic kinematic and Galilean relativity equations. The solution in the book assumes that the relative speeds are not the same in the two cases, with the relative speed being given by Vrelative=V1+V2 in the first case and Vrelative=V1-V2 in the second case. This is due to the fact that the motion of each body has acceleration,
CherryWine

Homework Statement

Two bodies are moving on the same line. When they move away from each other the distance between them changes for 16m in a time interval of 3 s (Δd1 = 16 m ; Δt1 = 3 s). When they move towards each other the distance between them changes for 3 m in a time interval of 3 s (Δd2 = 3 m ; Δt2 = 3 s). What are the respective speeds of the two bodies?

Homework Equations

Basic kinematic and Galilean relativity equations.

The Attempt at a Solution

So, I've reasoned that if the speeds of the bodies are constant, then in both cases, whether they are moving towards or away each other, the relative speed should be the same, because in both cases it is given by Vrelative=V1+V2, since their respective velocity vectors point in different directions in both cases. From that it follows that if the relative speeds are the same in both cases, then this equality holds Δd1/ Δt1 = Δd2/Δt2 , but it obviously does not when the numbers given in the problem are plugged in.

The solution in the book assumes that the relative speeds are not the same in the two cases, saying that in the case when they move away from each other the relative speed is given by Vrelative=V1+V2 but however in the case when they move towards each other the relative speed is given by Vrelative=V1-V2 which I don't understand why.

It is wrong! Because the the motion of each body has acceleration. veclociy increases or decreases diferrence so that vrelative increases or descreses too. Your case just right when acceleration=0

Hamal_Arietis said:
It is wrong! Because the the motion of each body has acceleration. veclociy increases or decreases diferrence so that vrelative increases or descreses too. Your case just right when acceleration=0
What ?! The mentioned speeds/velocities are constant, meaning the acceleration is zero.

ahh sorry :) first they move to near. and after they catch they move to far. and v =v1+v2 in 2 cases

Hamal_Arietis said:
ahh sorry :) first they move to near. and after they catch they move to far. and v =v1+v2 in 2 cases
They do not "catch" in any case. Imagine that their initial distance is infinite. Mentioned scenarios are separate.

Sorry my English isn't good so i can't read this problem correctly. After used gg translation. I answer you that: When they move away the relative velocity v=v1+v2. End when they move towards v=v1-v2.

Did you studied about the vector? It is total vector formula. But if you didnt. You can see this solution:Suppose that v1>v2
Move away:the distance they move in denta t
s1=v1denta t; s2=v2 denta t=> denta d=s1+s2=(v1+v2)denta t
Move towards: denta d=s1-s2=(v1-v2) denta t
v1+v2 and v1-v2 are relative velocity in each case.

Hamal_Arietis said:
Did you studied about the vector? It is total vector formula. But if you didnt. You can see this solution:Suppose that v1>v2
Move away:the distance they move in denta t
s1=v1denta t; s2=v2 denta t=> denta d=s1+s2=(v1+v2)denta t
Move towards: denta d=s1-s2=(v1-v2) denta t
v1+v2 and v1-v2 are relative velocity in each case.
Can you please explain why would Δd = s1-s2 in the case of them moving towards? Suppose they move with the same velocity, thus they cover equal distances in equal time intervals, therefore by your reasoning Δd would be zero, when obviously it is not!

I think move towards means same direction. Two vector v1,v2 are the same direction.
if v1=v2 mean denta d=0 => the distance between two bodies dont
change. But in this problem v1 and v2 are different.

Hamal_Arietis said:
I think move towards means same direction. To vector v1,v2 are the same direction.
if v1=v2 mean denta d=0 => the distance between two bodies dont
change. But in this problem v1 and v2 are different.
The problem is only solvable if the "move towards" case is considered as both bodies moving in the same direction (only one of them facing the other). However, the problem arose since this is not clear from the text of the problem.

1. What is Galilean relativity?

Galilean relativity is a principle in physics that states that the laws of motion are the same for all observers in uniform motion. This means that the laws of physics are independent of the observer's frame of reference and do not change based on their relative velocity.

2. What is the problem with Galilean relativity?

The problem with Galilean relativity is that it does not hold true in all situations, particularly when objects are moving at very high speeds or in the presence of strong gravitational fields. In these cases, the laws of motion as described by Galilean relativity do not accurately predict the behavior of objects.

3. How was Galilean relativity disproven?

Galilean relativity was disproven by Albert Einstein's theory of special relativity, which expanded upon the principles of Galilean relativity and introduced the concept of the speed of light as a constant and the idea of space and time being relative to the observer's frame of reference.

4. What are the implications of this problem for our understanding of the universe?

The problem with Galilean relativity has significant implications for our understanding of the universe. It has shown us that the laws of physics are not absolute and can change based on the observer's frame of reference. This has led to the development of new theories, such as general relativity, to better explain the behavior of objects in extreme conditions.

5. How does this problem affect everyday life?

In everyday life, the problem with Galilean relativity is not noticeable as the speeds and gravitational fields we encounter are not extreme enough to deviate significantly from the laws of motion described by Galilean relativity. However, technologies such as GPS and particle accelerators rely on the principles of special and general relativity, which were developed to address the limitations of Galilean relativity.

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