Answer:
d2 = 3.97 light years.
Explanation:
speed of the first traveler (V1) = 0.7 c
distance if the star (d1) = 6.5 light years
speed of the second traveler (V2) = 0.9 c
applying the formula [tex]d1 = d x \sqrt{1 - \frac{v1^{2} }{c^{2} } }[/tex], where 'd' is the distance between the earth and the star measured by an observer from earth,
we can get the value of 'd' and subsequently get the length for the second traveler
[tex]6.5 = d x \sqrt{1 - \frac{(0.7c)^{2} }{c^{2} } }[/tex]
[tex]6.5 = d x \sqrt{1 - (0.7)^{2} }[/tex]
d = [tex]\frac{6.5}{\sqrt{1 - (0.7)^{2} }}[/tex]
d = 9.1 light years
the distance from an observer on earth is 9.1 light years
now the length of the second traveler would be
[tex]d2 = 9.1 x \sqrt{1 - \frac{(0.9c)^{2} }{c^{2} } }[/tex]
[tex]d2 = 9.1 x \sqrt{1 - (0.9)^{2} }[/tex]
d2 = 3.97 light years.
