Question

An observer on Earths sees spaceship 1 fly at 0.80c. 9 years later according to the observer on Earth, spaceship 2 flies by Earth at 0.80c, traveling in the same direction as the first. Both spaceships continue to travel with constant velocities.

1) An observer in spaceship 1 observes Earth to pass spaceship 2 ________ years after Earth passed spaceship 1.

a)7.2

b)10

c)12

d)15

e)20

An observer in spaceship 1 observes spaceship 2 to be ______ light-years away.

a)7.2

b)10

c)12

d)16

e)20

Answer 1

1.

In spaceship 1 frame of reference, earth is moving at speed 0.8c. If the time interval in earth's frame is , it will be observed as in spaceship 1 frame of reference.

In earth's frame the time interval between the arrival of spaceships 1 and 2 is 9 years, this time interval will be observed as 15 years in spaceship 1's frame. So, the observer in spaceship 1 will observe earth to pass spaceship 2 15 years after earth passed spaceship 1.

2.

In spaceship 1 frame the distance between spaceship 2 and spaceship 1 is the distance traveled by the earth in 15 years (which is the time when spaceship 2 reaches earth). Since earth is moving at speed 0.8c, the distance is