Velocites in Different Reference Frames

[monke]

Homework Statement

The Millenia is catching up to the Galaxa at a rate of 0.55c when the captian of the Millenia decides its time to fire a missle. He uses a laser range finder to determine the distance to Galaxa and then he fires a missle that is moving at a speed of 0.45c.

What speed does the Galaxa measure for a) the laser beam and b) the missle as they both approch the starship

Homework Equations

I believe i would be using the relativistic velocity transformation formula for this problem however I don't understand how it works.

v= V1+V2/(1+ V1V2/c^2)




Would i do the equation and solve for a value for the laser beam and then use that to find the value for the missle?

The Attempt at a Solution

I tried using the known values for V1 and V2 but i got an answer of 1 and i don't know if that makes sense.

Thank you In advance for any help :)

 

[anathema]

Thank you for your question. I would like to help you understand the relativistic velocity transformation formula and how it applies to this scenario.

The relativistic velocity transformation formula is used to calculate the velocity of an object as measured by an observer in a different reference frame. In this case, we have two reference frames - the Millenia and the Galaxa. The Millenia is moving at a velocity of 0.55c and the Galaxa is stationary. The captain of the Millenia measures the distance to the Galaxa using a laser range finder and then fires a missile that is moving at a velocity of 0.45c.

Let's take a closer look at the formula: v = (V1 + V2) / (1 + V1V2/c^2)

Here, v represents the velocity of the object as measured by an observer in a different reference frame. V1 represents the velocity of the object in its own reference frame, and V2 represents the velocity of the reference frame it is moving towards or away from. c is the speed of light, which is a constant.

To answer your question, we need to plug in the values for V1 and V2. V1 is the velocity of the missile, which is 0.45c. V2 is the velocity of the Galaxa, which is 0.55c. Plugging these values into the formula, we get:

v = (0.45c + 0.55c) / (1 + (0.45c)(0.55c)/c^2)
v = (1c) / (1 + 0.2475)
v = 0.8c

So, the Galaxa would measure the velocity of the missile as 0.8c as it approaches the starship.

Now, let's find the velocity of the laser beam. In this case, V1 is the velocity of the laser beam, which is the speed of light (c). V2 is the velocity of the Millenia, which is 0.55c. Plugging these values into the formula, we get:

v = (c + 0.55c) / (1 + (c)(0.55c)/c^2)
v = (1.55c) / (1 + 0.55)
v = 0.91c