Two people stand a distance L apart along an east

Expert Solution

Considering the instant when the eastern person claps (in our time frame)

we are at L distance from the eastern person (next to western person), light has travelled a distance of L units at a speed of c. so the instant at which the person actually clapped (or in ground frame) was L/c units ago.

now L/c units of time ago we were at a distance (L/c)*(4c/5) = 4L/5 units west of the western person.

from this instant, we travelled at a speed of 4c/5 towards the western person and the light travelled at a speed of c towards us. so the speed of light (in our frame) is 4c/5 + c = 9c/5. the instant (in our frame) when we see the western person clap light has travelled a distance of 4L/5 (that is the distance between us and western person when he clapped... as we derived above).

so time difference in the instant the western person claps (in our frame and ground frame) = (4L/5) / (9c/5) = 4L/9c

in ground frame the distance travelled by the light in this duration (it is the same distance as the tree from the western person) = c * 4L/9c = 4L/9

so tree is 4L/9 units west (as we are traelling east) of the western person

genius_generous answered 4 weeks ago

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