How Do Velocities Combine in Relativistic Physics?

[Yukz23]

Homework Statement
Spacecraft 1 is launched from the surface of the Earth with a velocity of 0:6c (Earth
RF) at an angle of 50

above the horizontal +x axis. Spacecraft 2 is moving with a
velocity of 0:7c (Earth RF) in the x direction towards Spacecraft 1. Determine the
velocity and speed of Spacecraft 1 as measured by the pilot of Spacecraft 2.

The attempt at a solution
I'm trying to solve this and I'm stuck a bit so far all I've got is that
Vs1e (velocity of spacecraft 1 respect to earth) = 0.6cos50(c)
Vs2e = -0.7c

they want Vs1s2 = Vs1e + Ves2/ 1 + Vs1e (Ves2)/c^2

I'm stuck because I don't know what "Ves2" would be...

Thanks in advance

 

[Simon Bridge]

Welcome to PF;
I can't tell either ... I hate subscripts.

In the E frame:
Craft 1 has an x and a y component.
Craft 2 only has an x component.

Use the formula on each component to find the relative velocity of frames 1 and 2.

 

[Yukz23]

Lol Thanks,

So should I first do the formulas for the x components and the y components and then combine it..and the hypotenuse would be the answer?

 

[Simon Bridge]

Well... one of the directions does not matter.
Remember the derivation of time dilation you did a while ago - only one of the directions counted for that too.

 

[paranormal]

for any help.Hello, thank you for your question. I am a scientist and I would be happy to provide a response.

First, let's define our variables to make things clearer. Vs1e will represent the velocity of spacecraft 1 with respect to the Earth, Vs2e will represent the velocity of spacecraft 2 with respect to the Earth, and Vs1s2 will represent the velocity of spacecraft 1 as measured by the pilot of spacecraft 2.

Based on the given information, we can calculate the velocity of spacecraft 1 as measured by the pilot of spacecraft 2 using the velocity-addition formula:

Vs1s2 = (Vs1e + Vs2e) / (1 + Vs1e*Vs2e/c^2)

Since we know that Vs1e = 0.6c and Vs2e = -0.7c, we can plug these values into the formula and calculate the velocity of spacecraft 1 as measured by the pilot of spacecraft 2:

Vs1s2 = (0.6c - 0.7c) / (1 + (0.6c * -0.7c)/c^2)

= -0.1c / (1 - 0.42)

= -0.1c / 0.58

= -0.1724c

Therefore, the velocity of spacecraft 1 as measured by the pilot of spacecraft 2 is -0.1724c, or 17.24% of the speed of light in the negative x direction.

To calculate the speed of spacecraft 1 as measured by the pilot of spacecraft 2, we can simply take the absolute value of the velocity:

Speed of spacecraft 1 as measured by the pilot of spacecraft 2 = |-0.1724c| = 0.1724c

Therefore, the speed of spacecraft 1 as measured by the pilot of spacecraft 2 is 0.1724c, or 17.24% of the speed of light.

I hope this helps with your understanding of the problem. If you have any further questions, please do not hesitate to ask. Keep up the good work in your studies of modern physics!