# Solving for relativistic velocity using Newtonian physics

• gtguhoij
In summary, the conversation discusses the calculation of time and velocity for two cars approaching each other. The answer is provided as tD = [D_0 - 3/4ct - 1/2ct] and there is confusion about the use of "td". The expert clarifies that the mutual speed of the cars is 1.25c and explains how to calculate the time for them to crash into each other. The expert also mentions the relativistic composition of velocities and provides further clarification on calculating the contracted distance and determining the time for collision.
gtguhoij
Homework Statement
Here is another exercise focusing on how the distance, or gap, between two objects changes over time. If a taxi is racing toward you from the north at 3/4 light speed, and another taxi is racing toward you from the south at 1/2 light speed, how quickly from your perspective is each taxi approaching the other?
Relevant Equations
d = vt

The answer is tD = [D_0 - 3/4ct - 1/2ct] I just have 2 questions.

I realize for 2 vectors approaching it is negative for distance and for velocity positive. What be the rule for time? How do I find vector answers for velocity and distance and time?

I am confused why I have "td = ..." ? Can someone explain? "td" doesn't even make sense.

Leave vectors aside. You are one single observer; for you, the “mutual “ speed (wording used by W. Rindler in his book on relativity) by which the given distance between cars ( consider them as material points) decreases is simply :

##v = 0.75c +0.5c =1.25c##

no wonder that this result is greater that ##c##. No relativistic composition of speeds is to be made here. This is the answer to “how quickly...”.
So, if you are given the initial distance of the cars , simply divide it by that mutual speed, and this is the time for them to crash into each other, according to your wrist watch.
Be careful, don’t stay on their trajectory, if you don’t want to be reduced into a bloody steak.
But the point where they meet isn’t probably your original position .

Last edited:
gtguhoij
I ‘ ll add another clarification. The relativistic composition of velocities applies here if taxi driver A wants to know what is the speed of taxi B relative to him. The result is less than ##c##, as can be easily verified: 0.909c (approx).
Which is the wrist watch time for collision, for both A and B?
Determine the ##\gamma ## factor using the speed just found .
Determine the contracted distance ##\frac{D}{\gamma}## between cars.
Divide this contracted distance by the relativistic speed, and you are done.

gtguhoij

## 1. How is relativistic velocity different from classical velocity?

Relativistic velocity takes into account the effects of special relativity, such as time dilation and length contraction, while classical velocity does not. This means that as an object approaches the speed of light, its relativistic velocity will increase at a slower rate than its classical velocity.

## 2. Can Newtonian physics accurately calculate relativistic velocity?

No, Newtonian physics is only valid for objects moving at speeds much slower than the speed of light. At high speeds, the predictions of Newtonian physics do not match with experimental results and must be replaced with the principles of special relativity.

## 3. How do you incorporate time dilation into the calculation of relativistic velocity?

In order to incorporate time dilation, the concept of proper time must be used. Proper time is the time experienced by an object in its own frame of reference. In the calculation of relativistic velocity, proper time replaces the time variable in the classical velocity equation.

## 4. Is there a limit to how fast an object can travel using Newtonian physics?

Yes, according to Newtonian physics, the speed of light is the ultimate speed limit. As an object approaches the speed of light, its mass and energy increase infinitely, making it impossible to reach or exceed the speed of light.

## 5. How does the concept of length contraction affect the calculation of relativistic velocity?

Length contraction is the phenomenon in which an object appears shorter in the direction of its motion relative to an observer. In the calculation of relativistic velocity, the contracted length is used instead of the actual length in the classical velocity equation.

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