Understanding Velocity Transformation

[Zeeshan Ahmad]

Homework Statement

If earth observer sees 1.5c speed
Ship observer see 0.7c
Compute their speeds for earth observer
The complete statement of the question is in the Relevant equation section

I would like have to solution this problem

Relevant Equations

Two spaceships approach each other with 1.5 c (Galilean addition of velocities), according to an observer on earth. The speed of one of these spaceships measured by other's pilot is 0.75 c. Compute their speeds for the observer on earth.

I have used velocity transformation ibut a little confused on it so do solve the problem

 

[haruspex]

Homework Statement:: If Earth observer sees 1.5c speed
Ship observer see 0.7c
Compute their speeds for Earth observer
The complete statement of the question is in the Relevant equation section

I would like have to solution this problem
Relevant Equations:: Two spaceships approach each other with 1.5 c (Galilean addition of velocities), according to an observer on earth. The speed of one of these spaceships measured by other's pilot is 0.75 c. Compute their speeds for the observer on earth.

I have used velocity transformation ibut a little confused on it so do solve the problem

As per forum rules, please post your working so far.
The problem statement belongs in the "homework statement " section. "Relevant equations" is for standard equations relevant to the topic, such as relativistic velocity addition.

 

[Zeeshan Ahmad]

This the solution i have done so far

 

[PeroK]

Relevant Equations:: Two spaceships approach each other with 1.5 c (Galilean addition of velocities), according to an observer on earth. The speed of one of these spaceships measured by other's pilot is 0.75 c. Compute their speeds for the observer on earth.

Are you sure about those numbers?

 

[PeroK]

This the solution i have done so far
View attachment 298947

This doesn't look like a solution to the problem as stated.

 

[haruspex]

This the solution i have done so far
View attachment 298947

Please define all your variables. Otherwise it may be impossible to pinpoint the error.

 

[Zeeshan Ahmad]

Are you sure about those numbers?

Its 0.7c and 1.5 c in statement typing mistake

 

[PeroK]

Its 0.7c and 1.5 c in statement typing mistake

I don't see how those numbers can work out. If one ship measures the speed of the other as $0.7c$, then the combined speed of approach in the Earth frame must be less than $1.4c$.

The question looks wrong to me.

 

[PeroK]

Here's my analysis. We know that the combined speed of approach is $1.5c$. If the rockets have speeds $v_1$ and $v_2$ in the Earth frame, then $v_1 + v_2 = 1.5c$.

First, we could have $v_1 = v_2 = 0.75c$. This gives the speed of either rocket measured by the other rocket as $0.96c$, which is what you have calculated. Or, in fact, you assumed $0.7c$ and $0.8c$, which gives a similar answer.

As we increase the speed $v_1$, the measured speed increases. Eventually, if $v_1 \approx c$ and $v_2 \approx 0.5c$, then the measured speed is approximately $c$.

It can never be less than $0.96c$, let alone $0.75c$.

That's why the problem cannot be as stated.