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# Answer to Question #125381 in Mechanics | Relativity for numan

Question #125381
A rod of length Lo = 1m, moves with speed v equivalent to 77% of the speed of light c along the y-axis direction. At rest, the rod makes an angle of 35 ° with respect to the x- axis.
a) Determine the length of the rod as measured by a stationary observer.
b) Determine the angle θ the rod makes with the x axis when it reaches its speed.
1
2020-07-06T15:12:54-0400

a). Since, initially angle made with x axis is "35^\\circ" thus

"L_{ox}=1\\cdot\\cos(35^\\circ)=0.82m\\\\\nL_{oy}=1\\cdot\\sin(35^\\circ)=0.57m\\\\"

As there is only motion along y axis, and "v=\\frac{77}{100}c"

"L_y=\\frac{L_{oy}}{\\sqrt{1-v^2\/c^2}}\\implies L_y=0.89m"

Thus,

"L=\\sqrt{L_y^2+L_{ox}^2}=1.21m"

b)Now,

"\\theta=\\tan^{-1}(L_y\/L_{0x})=47.34^\\circ"

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