Answer
(a) $p = 6.7\times 10^9~kg~m/s$
(b) $t = 1.6\times 10^7~s$
Work Step by Step
(a) We can find the momentum:
$p = \gamma~m~v$
$p = \frac{1}{\sqrt{1-\frac{v^2}{c^2}}}~m~v$
$p = \frac{1}{\sqrt{1-\frac{(0.87~c)^2}{c^2}}}~(12.6~kg)~(0.87~c)$
$p = \frac{1}{\sqrt{1-(0.87)^2}}~(12.6~kg)~(0.87)(3.0\times 10^8~m/s)$
$p = 6.7\times 10^9~kg~m/s$
(b) We can find the required time the force must be applied:
$F~t = p$
$t = \frac{p}{F}$
$t = \frac{6.7\times 10^9~kg~m/s}{424.6~N}$
$t = 1.6\times 10^7~s$
