Considering length of the stick as the Hypotenuse of Right Angled Triangle, we have-
Length of stick along x-axis = 1"\\times" cos30°
= "\\frac{\\sqrt{3}}{2}" m
Since motion is along x-direction, length contraction will also take place along x direction only. Therefore,
lx = lox"\\sqrt{1-\\frac{v^2}{c^2}}"
= lox"\\sqrt{1-0.4225}"
= lox (0.76)
= 0.658m
ly = loy
= sin30°
= 0.5m
Length of stick in the moving frame-
= "\\sqrt{0.5^2+0.658^2}"
= 0.8264 m
The 1m long stick is contracted to 0.8264m in the moving frame
Now,
Angle stick make with x-axis-
"\\theta" = tan-1("\\frac{0.5}{0.658}" )
= 37.23°
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