Answer:
a. speed, v = 0.97 c
b. time, t' = 20.56 years
Given:
t' = 5 years
distance of the planet from the earth, d = 10 light years = 10 c
Solution:
(a) Distance travelled in a round trip, d' = 2d = 20 c = L'
Now, using Length contraction formula of relativity theory:
(1)
time taken = 5 years
We know that :
time =
5 = (2)
Dividing eqn (1) by v on both the sides and substituting eqn (2) in eqn (1):
Squaring both the sides and Solving above eqution, we get:
v = 0.97 c
(b) Time observed from Earth:
Using time dilation:
Solving the above eqn:
t'' = 20.56 years