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## Homework Statement

Special Relativity Question.

Consider objects 1 and 2 moving in the lab frame; they both start at the origin, and #1 moves with a speed u and #2 moves with a speed v. They both move in straight lines, with an angle θ between their trajectories (again in the lab frame). What is #1's speed as viewed by #2?

## Homework Equations

x' = γ(x-vt)

t' = γ(t-(vx/c

^{2}))

u' = (u±v)/(1±(uv/c

^{2}))

Length Contractions

Lorentz Transformations

[/B]

Where γ = 1/((1-(v

^{2}/c

^{2}))),

v is the velocity of the frame S' relative to S,

and u' is the velocity of some object in the new frame S'.

(These are general equations, not variables from the question).

## The Attempt at a Solution

So I assumed the lab frame (I'll call it S) was at rest, and I had #2's (Flash) velocity along the x-axis, and #1's (Superman) velocity at some angle θ

_{1}above that, both starting from the origin. To simplify things, I made another frame S' where the new V

_{frame}=v, so in this new frame object 2's speed is v' = 0, and u' is what we're looking for I think.

In the

*j*direction, nothing would change in S' for object 1, and the velocity in the

*i*direction would be less so the angle would change, as well as the magnitude from that, so we now have θ

_{2}. However, I'm not really sure how I would use this new angle. From using the

**u'**equation I have above, I got:

u'

_{x}= (u*cos(θ

_{1}) - v) / (1 - (u*cos(θ

_{1})*v / (c

^{2})))

(Would this be 1+ uc/c^2 or 1- uv/c^2 in the denominator? I'm not sure how to tell)

u'

_{y}= (u*sin(θ

_{1}) - 0) / (1 - 0)

I got 1 - 0 because the V of the frame in the

*j*direction is 0

However none of that really took into account θ

_{2}, and I'm not sure how to get my final answer with the x and y components. With relativity can I just do the Pythagorean theorem as normal?