1. Three spaceships, A, B and C, pass the Earth, E, at a speed of v= 4c/ 5, wher

Question

1. Three spaceships, A, B and C, pass the Earth, E, at a speed of v= 4c/ 5, where c is the speed of light. The ships are 9x10^11

meters apart in the rest frame of the ships. When spaceship B is passing Earth, spaceships A and C emit light pulses simultaneously according to observers in Earths frame of reference. In Earth's frame, set the time to zero when these

events occur; set the time in the spaceships' frame to zero at the moment when spaceship B is passing Earth.

          E

A        B          C

(a) According to observers in Earth's frame, how far apart are the ships?

(b) According to observers in Earth's frame, at what time do the pulses arrive at earth?

(c) According to spaceship B, what is the speed of each pulse?

(d) Draw a plot of ct vs x showing the positions of the three spaceships and of the light pulses vs. time, in Earth's frame. Find the times, according to the Earth frame, at which the pulses from ships C and A reach ship B.

Explanation / Answer

1. let us assume that the aircraft A was at distance Dm when the light that is emmited from it reaches at the observer at time t=0. Then distance travelled by the light = Dm and distance travelled by the spaceship= D-9x10^11m now the time is same

so D/c = (D-9x10^11)/(4c/5) or D=36x10^11m

now assume that the aircraft C was at distance Dm when the light that is emmited from it reaches at the observer at time t=0. Then distance travelled by the light = Dm and distance travelled by the spaceship= 9x10^11-Dm now the time is same

so D/c = (9x10^11-D)/(4c/5) or D=4x10^11m

2. the pulses will arrive at t=9x10^11/(3x10^8)=3000sec=50mins

3. In the frame of spacecraft B A and C are stationary so the velocities of the pulses will be only c or 3x10^8 m/s .

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