Calculating Distance in Galilean Transformations

In summary, a bus is traveling at a constant speed of 24 m/s down a straight highway. The driver puts on her sunglasses, and 3.5 seconds later, a passenger sitting 5 m behind her drops a pen. To determine the distance between these events in the frame of reference of the earth, a measuring tape can be placed inside the bus and another on the street to determine the positions of the events relative to each coordinate system.
  • #1
aaku516
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Homework Statement


A bus travels forward at a constant speed of 24 m/s down a straight highway. the driver puts on her sunglasses, and 3.5 s later, a passanger stiing 5 m behind her drops a pen. In the frame of reference of the earth, what is the distance seprating these events?


Homework Equations


x = x' + vt
Δx = Δx' + vΔt
u = u' + v

a = a'


The Attempt at a Solution


Ahh Cannot understand this problem, the part of "relative to the earth" confuses me!
 
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  • #2
Suppose that we put a measuring tape inside the bus, with the x = 0 position below the driver seat. Then "relative to the bus", i.e. with respect to this tape, the first even happens at x = 0 and the other event happens at x = 5, right?

Now put a similar measuring tape on the street, exactly such that the driver passes over the x = 0 position as she puts on her sunglasses. At what position with respect to this coordinate system is the passenger that drops the pen 3.5 seconds later?
 

Related to Calculating Distance in Galilean Transformations

1. What are Galilean Transformations?

Galilean Transformations are a set of equations that describe how physical measurements (such as time, distance, and velocity) appear to change when viewed from different frames of reference. They were first developed by Galileo Galilei in the 17th century and are still used in classical physics today.

2. How do Galilean Transformations differ from Einstein's Theory of Relativity?

While both Galilean Transformations and Einstein's Theory of Relativity deal with the way measurements change in different frames of reference, they have different assumptions and implications. Galilean Transformations assume that time and space are absolute and that the laws of physics are the same in all frames of reference, while Einstein's Theory of Relativity takes into account the effects of gravity and the speed of light on measurements.

3. What is the purpose of Galilean Transformations?

The purpose of Galilean Transformations is to simplify calculations and make it easier to describe the motion of objects in classical physics. By using these equations, scientists can transform measurements from one frame of reference to another and still accurately describe the physical phenomena being observed.

4. Can Galilean Transformations be applied to all types of motion?

No, Galilean Transformations are only applicable to constant velocity motion. This means that they cannot accurately describe the motion of objects that are accelerating or moving at speeds close to the speed of light. In these cases, Einstein's Theory of Relativity must be used.

5. How do Galilean Transformations impact our understanding of the universe?

Galilean Transformations have played a significant role in the development of classical physics and our understanding of the laws of motion. They have also been used in fields such as astronomy, mechanics, and engineering to make accurate predictions and calculations. However, with the advent of modern physics and the theory of relativity, their limitations have become apparent and they are no longer considered a complete description of the universe.

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