Answer
a) $0.765\frac{m}{s}$
b) $l_0=0.21m$
Work Step by Step
a) $E_K=(\gamma-1)mc^2=14,000mc^2$
$\frac{1}{1-\frac{v^2}{c^2}}=\bigg(\frac{E_K}{mc^2}+1\bigg)^2$
$v=c\sqrt{1-\frac{1}{\bigg(\frac{E_K}{mc^2}+1\bigg)^2}}$
$v=c\sqrt{1-\frac{1}{\bigg(\frac{14000mc^2}{mc^2}+1\bigg)^2}}$
$v=c\sqrt{1-\frac{1}{14001^2}}=0.99999999744934c$
$c-v=c(1-0.99999999744934)=0.765\frac{m}{s}$
b) $l_0=l\sqrt{1-\frac{v^2}{c^2}}=(3.0\times10^3m)\sqrt{\frac{1}{14001^2}}=0.21m$
