The proper length of spaceship A is 60.0m and the proper length of spaceship B is 120.0m. The proper mass of spaceship A is 15000 kg. An observer on Earth watches the two spaceships fly past at a constant speed and determines that they have the same length. If the speed of the slower ship is 0.70c, find:
a) The length of spaceship A, relative to an observer on earth
b) The length of spaceship B, relative to an observer on earth
c) The mass of spaceship A, relative to an observer on earth.
Lm = Ls √(1- v2 / c2
mm = ms / √(1- v2 / c2
The Attempt at a Solution
Since both ships appear to have the same length to the observer on earth, ship A must be traveling faster than ship B as length contraction becomes more apparent with an increase in speed: In order for the two uneven length ships to appear the same, they must be moving at different speeds, and B must be the slower ship, therefore the velocity of B is 0.70c.
a) Lm = Ls √(1- v2 / c2
Lm = 60.0m √(1- 0.70c2 / c2
Lm = 60.0m √ (1- 0.49)
Lm = 42.85
Lm = 43m
The length of spaceship A, relative to an observer on Earth is 43m.
For a), I am unsure how to determine the velocity of ship B, other than trying multiple values until ship B's length matches that of ship A. I know there must be some way to determine the velocity of B, I just can't think of it. That value is also required to determine the relativistic mass of spaceship B, so any help on how to determine that value would be great.