All Problems Relativistic Mechanics
Problem 1.343
A stationary upright cone has a taper angle \(\theta=45^{\circ}\), and the area of the lateral surface \(S_{0}=4.0 \mathrm{~m}^{2}\). Find: its taper angle; (b) its lateral surface area, in the reference frame moving with a velocity \(v=(4 / 5) c\) along the axis of the cone.
1.343. (a) \(\tan \theta^{\prime}=\frac{\tan \theta}{\sqrt{1-\beta^{2}}} .\) Hence \(\quad \theta^{\prime}=59^{\circ}\); (b) \(S=\) \(=S_{0} \sqrt{1-\beta^{2} \cos ^{2} \theta}=3.3 \mathrm{~m}^{2}\). Here \(\beta=v / c\)