- #1
Aziza
- 190
- 1
An observer on Earth observes two spacecraft moving
in the same direction toward the Earth. Spacecraft A appears
to have a speed of 0.50c, and spacecraft B appears
to have a speed of 0.80c. What is the speed of spacecraft
A measured by an observer in spacecraft B?So if S is the reference frame of the Earth, S' is the reference frame of plane B, v is the velocity with which S' approaches S (according to S), u is the velocity with which plane A approaches Earth (according to Earth) and u' is the velocity with which plane A approaches plane B (according to B), then:
v = -0.8c
u = -0.5c
u' = (u-v) / 1-(uv/c2)) = 0.5c
I am interpreting this as meaning that according to plane B, plane A is actually moving away from B at 0.5c. My book, however, has the answer as -0.5c, implying the opposite, i think?...is the book wrong or are my signs wrong? It makes sense to me making v and u negative because the formula for the velocity transformation was derived assuming that S' and the event (plane A here) are moving away from S, not towards...
in the same direction toward the Earth. Spacecraft A appears
to have a speed of 0.50c, and spacecraft B appears
to have a speed of 0.80c. What is the speed of spacecraft
A measured by an observer in spacecraft B?So if S is the reference frame of the Earth, S' is the reference frame of plane B, v is the velocity with which S' approaches S (according to S), u is the velocity with which plane A approaches Earth (according to Earth) and u' is the velocity with which plane A approaches plane B (according to B), then:
v = -0.8c
u = -0.5c
u' = (u-v) / 1-(uv/c2)) = 0.5c
I am interpreting this as meaning that according to plane B, plane A is actually moving away from B at 0.5c. My book, however, has the answer as -0.5c, implying the opposite, i think?...is the book wrong or are my signs wrong? It makes sense to me making v and u negative because the formula for the velocity transformation was derived assuming that S' and the event (plane A here) are moving away from S, not towards...