What Is the Length of a Meter Stick Moving at an Angle?

[SpaceTrekkie]

Homework Statement

A meter stick is moving with 0.8C relative to frame S. What is the sticks length when measured by an observer in S if the stick is 60 degrees to v, as seen in the rest frame?

Homework Equations

Length contraction = proper length /lorentz factor

The Attempt at a Solution

Okay for the speed I got the lorentz factor = 1.66667. So if the meter stick was moving directly parallel the length would be contracted to .6 meters. I know that length contraction only occurs in the direction of motion, so NOT perpendicular. And I know that I can solve it by thinking about the meter stick as the hypotenuse of a 30-60-90 triangle. I think I am just mis visualizing something, but I really can't seem to work it out. I looked in the back of the book and the answer is .917 meters. I used that to try to work backwards and still could not figure it out.

Any direction would be awesome...

 

[tiny-tim]

Hi SpaceTrekkie!

Okay for the speed I got the lorentz factor = 1.66667.
So if the meter stick was moving directly parallel the length would be contracted to .6 meters. I know that length contraction only occurs in the direction of motion, so NOT perpendicular.
And I know that I can solve it by thinking about the meter stick as the hypotenuse of a 30-60-90 triangle.

All correct.

Draw the triangle in x,y coordinates.

Now draw it again in x',y' coordinates.

y' = y and x' = 0.6x, so … ?

 

[SpaceTrekkie]

Hmm, Does it work to change the x and y-axis so that they x-axis is in like with the direction of motion? I think that might make it easier, or am I over thinking the problem?

 

[tiny-tim]

Hmm, Does it work to change the x and y-axis so that they x-axis is in like with the direction of motion? I think that might make it easier, or am I over thinking the problem?

No, you're completely correct …

always have one of the axes in the direction of motion …

otherwise the equations get too complicated!