Problem 16.41 Challenge

พิจารณาความยาวตามแนวแกน x

จาก \(Δx = \frac{\Delta x_{0}}{\gamma}\)

\(\Delta x_{0} = \gamma \Delta x\)

\(\Delta x_{0} =\frac{\Delta x}{1 -\frac{v^{2}}{c^{2}}}\)

\(\Delta x_{0} =\frac{(2.00 m)\cos (30.0°)}{1 -\frac{(0.995c)^{2}}{c^{2}}}= 17.34 m\)

พิจารณาความยาวตามแนวแกน y

จาก \(Δy_{0} = Δy = (2.00)sin(30.0°) = 1.00 m\)

\(\therefore \Delta L_{0} =\sqrt{\Delta x_{0}^{2} + \Delta y_{0}^{2}}\)

\(\Delta L_{0} =\sqrt{(17.34 m)^{2} + (1.00)^{2}}= 17.4 m \;\blacksquare\)

\(\therefore \theta _{0} = \tan ^{-1}(\frac{\Delta y_{0}}{\Delta x_{0}})\)

\(\theta _{0} = \tan ^{-1}(\frac{1.00 m}{17.34 m})\)

\(\theta _{0} = 3.30° \;\blacksquare\)