1. A 22 year-old biologist makes a trip to study life forms in a distant planet
ID: 1998425 • Letter: 1
Question
1. A 22 year-old biologist makes a trip to study life forms in a distant planet 17 light-years away. The round trip including a stay of 1 year in the distant planet takes 38 years according to the clock on earth. The biologist's son is 2.5 year-old when she left. Assume that the planet is not moving with respect to earth. How fast is the spaceship traveling? Give your answer in terms of the speed of light. You do not need to enter "c" as unit.
2. How old is she when she returns according to her clock?
3.How old is her son according to the clock on earth?
4. What is the total distance traveled according to the biologist? Give your answer in light-years. You do not need to enter the units.
Explanation / Answer
distance traveled as measured on earth = 2 * 17 L-y = 34 L-y
time traveled at speed v = time for light to travel same distance
37 * v = 34 *c
v / c = 34 / 37
v / c = 0.92
v = 0.92 c
Let = (1 - v2 / c2)
= 0.394
= T
where is the proper time as measured by the clock at rest in the spaceship
The time spent in travelling as measured on the spaceship is
= 37 * 0.394
= 14.6 years
So the biologist ages 14.6 + 1 = 15.6 years
The biologist is then 22 + 15.6 = 37.6 years old
Her son ages 38 years according to a clock on earth and is then 38+2.5 = 40.5 yrs old
The total proper distance traveled (measured on earth) is
L = L0 = 34 L-y
and
The total distance traveled as measured on the moving spaceship
L = L0
L = 34 * 0.394
= 13.4 L-y
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