Answer:
28.82 minutes
Explanation:
This problem is an example of time dilatation by acceleration. The formula is:
[tex]\Delta t=\gamma \Delta t_0=\frac{\Delta t_0}{\sqrt{1-\frac{v^2}{c^2} }}[/tex]
[tex]\Delta t[/tex] is the time measured by the observer on a fixed position (in this case in the fixed planet), [tex]\Delta t_0[/tex] is the time measured by the person moving away from the fixed observer (the one on an interplanetary express bus), [tex]c[/tex] is the speed of light and [tex]v[/tex] the velocity of the observer that is moving away (the velocity of the ship).
[tex]\Delta t_0=9 min=540s\\\Delta t=\frac{540}{\sqrt{1-\frac{(0.95c)^2}{c^2}}}=\frac{540}{\sqrt{1-\frac{0.95^2c^2}{c^2}}}=\frac{540}{\sqrt{1-0.95^2}}\\\Delta t=\frac{540}{\sqrt{1-0.9025}}=\frac{540}{\sqrt{0.0975}}=\frac{540}{0.3122}=1729.38s\\\Delta t=28.82minutes[/tex]
