Aspace traveler moving at a speed of 0.70c with respect to the earth makes a trip to a distant star that is stationary relative to the earth. he measures the length of this trip to be 6.5 light-years. what would be the length of this same trip (in light-years) as measured by a traveler moving at a speed of 0.90c with respect to the earth?

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 , 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

d =

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

d2 = 3.97 light years.