W zadaniu należy skorzystać z transformacji Lorentza: [latex]Delta t=0,12s\ Delta t_0=0,1s\ c=3*10^8frac{m}{s}\\ Delta t=gammaDelta t_0, gdzie gamma=dfrac{1}{sqrt{1-frac{v^2}{c^2}}}leftarrow czynnik Lorentza\\\ Delta t=dfrac{Delta t_0}{sqrt{1-frac{v^2}{c^2}}}\\\ Delta t^2=dfrac{Delta t_0^2}{1-frac{v^2}{c^2}}}\\\ [/latex] [latex]Delta t^2(1-frac{v^2}{c^2})=Delta t_0^2\\ Delta t^2-frac{Delta t^2 v^2}{c^2}=Delta t_0^2\\ frac{Delta t^2 v^2}{c^2}-Delta t^2=-Delta t_0^2\\ frac{Delta t^2 v^2}{c^2}=Delta t^2-Delta t_0^2\\ Delta t^2 v^2=c^2(Delta t^2-Delta t_0^2)\\ v^2=frac{c^2(Delta t^2-Delta t_0^2)}{Delta t^2}\\ oxed {v=sqrt{dfrac{c^2(Delta t^2-Delta t_0^2)}{Delta t^2}}}\\[/latex] Podstawiamy dane i obliczamy: [latex]v=sqrt{dfrac{(3cdot10^8)^2(0,12^2-0,1^2)}{0,12^2}}\\\ v=sqrt{dfrac{9cdot10^{16}(0,0144-0,01)}{0,0144}}\\\ v=sqrt{dfrac{9cdot10^{16}cdot0,0044}{0,0144}}\\\ v=sqrt{2,75cdot10^{16}}\\ oxed{vapprox 1,658cdot 10^8frac{m}{s}}[/latex] Pozdrawiam, Adam
