Key 6 - properHoc

Forward moving:
$\displaystyle w=\frac{{u+v}}{{1+\frac{{uv}}{{{{c}^{2}}}}}}=\frac{{0.7c+0.8c}}{{1+\frac{{0.8c\cdot 0.7c}}{{{{c}^{2}}}}}}=\frac{{0.7+0.8}}{{1+0.8\cdot 0.7}}c=0.9615c$
Moving toward the back:
$\displaystyle w=\frac{{u+v}}{{1+\frac{{uv}}{{{{c}^{2}}}}}}=\frac{{-0.7c+0.8c}}{{1-\frac{{0.8c\cdot 0.7c}}{{{{c}^{2}}}}}}=\frac{{-0.7+0.8}}{{1-0.8\cdot 0.7}}c=0.2272c$
$\displaystyle w=\frac{{c+c}}{{1+\frac{{c\cdot c}}{{{{c}^{2}}}}}}=\frac{{2c}}{2}=c$

Last modified: Jun 10, 2025 @ 15:51