Suppose that we are able to accelerate a space ship using a force equal to mgmg$,$ where mm is the mass of the space ship $($including the passengers and all other contents$),$ and g$=9\mathrm{.}80$g$=9\mathrm{.}80$m$/$s$22.$ In the reference frame of the space ship, this force would always produce an acceleration equal to$$gg$,$ and the passengers would feel as though they were in a gravitational field equal to that on the surface of the Earth. In the Earth's reference frame, however, the acceleration of the space ship would decrease as its speed approaches the speed of light. Answer all parts of this problem relative to the Earth's frame of reference.

$($a$)$

If m$=187000$m$=187000$kg$,$ find the momentum of the space ship when it reaches a speed of $0\mathrm{.}99144$cc$.$

kg$$m$/$s $(5$E$12$ kg$$m$/$s$)$

$($b$)$

Using F$=$p$/$tF$=$p$/$t $($force equals the change of momentum per unit time$),$ calculate how long it takes to reach this speed.

y $(0\mathrm{.}05$ y$)$

$($c$)$

If the acceleration a$=$v$/$ta$=$v$/$t were really constant and equal to$$gg$,$ what would be the speed of the space ship after the amount of time found in part $($b$)?$ Give this speed in terms of the speed of light.

cc $(0\mathrm{.}05$ cc$)$