9-42 할리데이 11판 솔루션 일반물리학

$$ \put \begin{cases} m:\text{Mother}\\ d:\text{Daughter}\\ n:\text{neutrino}\\ e:\text{electron}\\ \end{cases} $$ $$ \begin{cases} p_m&=0\\ p_e&=-1.2\times10^{-22}\i\ut{kg\cdot m/s}\\ p_n&=-6.4\times10^{-23}\j\ut{kg\cdot m/s}\\ m_d&=5.8\times10^{-26}\ut{kg}\\ \end{cases} $$ $$ \begin{aligned} \vec p_m&= \vec p_d+ \vec p_e+ \vec p_n\\ \vec p_d&=-\vec p_e- \vec p_n\\ &=1.2\times10^{-22}\i+6.4\times10^{-23}\j\\ \end{aligned} $$ $$\ab{a}$$ $$ \begin{aligned} p_d&=\sqrt{(1.2\times10^{-22})^2+(6.4\times10^{-23})^2}\\ &=\frac{34}{25}\times10^{-22}\ut{kg\cdot m/s}\\ &=1.36\times10^{-22}\ut{kg\cdot m/s}\\ &\approx 1.4\times10^{-22}\ut{kg\cdot m/s}\\ \end{aligned} $$ $$\ab{b}$$ $$ \begin{aligned} \theta_d&=\tan^{-1}\frac{6.4\times10^{-23}}{1.2\times10^{-22}}\\ &=\tan^{-1}\frac{8}{15}\\ &\approx 0.4899573262537283\ut{rad}\\ &\approx 0.49\ut{rad}\\ \end{aligned} $$ $$\ab{c}$$ $$ \begin{aligned} \KE&=\frac{1}{2}mv^2\\ &=\frac{p^2}{2m}\\ &=\frac{(1.36\times10^{-22})^2}{2\cdot 5.8\times10^{-26}}\\ &=\frac{1156}{725}\times10^{-19}\ut{J}\\ &\approx 1.5944827586206898\times10^{-19}\ut{J}\\ &\approx 1.6\times10^{-19}\ut{J}\\ \end{aligned} $$