- #1

Ascendant0

- 109

- 26

- Homework Statement
- A meter stick is moving with speed 0.8c relative to frame S. What is the stick's length if the stick is at ## 60^{\circ} ## to its velocity v, as measured in frame S?

- Relevant Equations
- ## l = l_\circ / \gamma ##

I'm having a hard time since the angle is being measured in frame ##S##.

What I have put together so far is ## l_y = l_{y0} = 1m(sin(\theta_\circ)) ##

And ## l_x = l_{x0}/\gamma ##

Where ## l_{y0} ## and ## l_{x0} ## are the respective x and y values of the meter stick in the proper lengths (in ##S'## reference frame moving at the same speed as the meter stick)

I know the y values won't change because there's no movement in that direction. What I can't figure out is how to figure out what the angle would be in the ##S'## system, so I can find the proper angle to calculate the length based off that.

I tried using tan to relate the equations, but it hasn't gotten me anywhere yet. Help would be greatly appreciated, as I've been racking my brain on this one for a while, and just can't seem to figure it out.

What I have put together so far is ## l_y = l_{y0} = 1m(sin(\theta_\circ)) ##

And ## l_x = l_{x0}/\gamma ##

Where ## l_{y0} ## and ## l_{x0} ## are the respective x and y values of the meter stick in the proper lengths (in ##S'## reference frame moving at the same speed as the meter stick)

I know the y values won't change because there's no movement in that direction. What I can't figure out is how to figure out what the angle would be in the ##S'## system, so I can find the proper angle to calculate the length based off that.

I tried using tan to relate the equations, but it hasn't gotten me anywhere yet. Help would be greatly appreciated, as I've been racking my brain on this one for a while, and just can't seem to figure it out.