Answer:
The closeness to the speed of light is [tex]c -v_{min} =0.006000m/s[/tex]
Explanation:
From the question we are told that
The time taken to travel to Andromeda Galaxy is [tex]t_o = 2.54* 10^7 \ light -years[/tex]
The life time of human is [tex]t = 75 \ years[/tex]
Generally the life time of a human can evaluated mathematically as follows
[tex]t = t_o \sqrt{1 - \frac{v_{min}}{c^2} }[/tex]
Where t is the life time of human
Making [tex]v_{min}[/tex] the subject of the formula
[tex]v_{min} = [ \sqrt{1- (\frac{t}{t_o})^2 } ] c[/tex]
substituting values
[tex]v_{min} = [ \sqrt {1- {(\frac{75.0}{2.54*10^{7} })^2 } ]} c[/tex]
[tex]v_{min} = [ \sqrt{ 1 - 8.7202 *10^{-12}} ] c[/tex]
[tex]v_{min} = 0.99999999998 c[/tex]
The closeness of [tex]v_{min}[/tex] to the speed of light is mathematically evaluated as
[tex]c -v_{min} = c - 0.99999999998c[/tex]
[tex]c -v_{min} =( 1 - 0.99999999998) c[/tex]
substituting [tex]3.0*10^{8}m/s[/tex] for c
[tex]c -v_{min} =2.0*10^{-11} * 3.0*10^8[/tex]
[tex]c -v_{min} =0.006000m/s[/tex]
