A rocket train car that is 30 m long is traveling from Los Angeles to New York at v=0.5c when a light at the center of the car flashes. When the light reaches the front of the car, it immediately rings a bell. Light reaching the back of the car immediately sounds a siren. A bicyclist waiting to cross the tracks sees the light in front of her at the instant when it flashes. Choose frame S' so that its origin is located at the center of the train. Take the direction of motion of the train (eastward) to be the positive direction of x'. Let the instant when the light flashes be t′=0s. Required:
What are (x′A,t′A) and (x′B,t′B), the spacetime coordinates of event A and B in S'?

The reference frame of a passenger in a seat near the center of the train

Explanation:

the speed of light is the same for the passenger and the bicyclist

then the avents are simultaneous fo the passenger not for the bicyclist

the delay between the two events for the bicyclist is

Δt=Δd/vs

where

Δd= lenght of train

vs=speed of sound

the reference frame of a passenger in a seat near the center of the train

Solution:

The space and time transformations are:

x' = γ(x - vt)

t' = γ(t - vx/c²).

In the primed frame the two events are simultaneous, so that Δt' = 0. Also here Δx' = 30. In the unprimed frame Δx' = 30 = γ(Δx - v Δt)(*)

We also have Δt' = 0 = γ(Δt - vΔx/c²)→Δx = c²Δt/v(**)

Substituting (**) in (*): 30 = γ(c²Δt/v - vΔt))→Δt = 30/(c²/v - v) =

30/(2c - 0.5c) = 6.7 x 10^(-8)s

B. The bacteria would be relatively evenly distributed along the algal filaments.

Explanation:

A) There would be no difference in results.

B) The bacteria would be relatively evenly distributed along the algal filaments.

C) The number of bacteria present would decrease due to an increase in the carbon dioxide concentration.

D) The number of bacteria present would increase due to an increase in the carbon dioxide concentration.

E) The number of bacteria would decrease due to a decrease in the temperature of the water.

When different segments of light was used, largest groups of aerobic bacteria were found in the red and blue regions of light because these regions have been reported to be best efficient for photosynthesis and thus, oxygen production.

If the experiment is repeated without separating the light segment, one would expect a somehow uniform distribution of aerobic bacteria growth along the algal segment since the different light segments in white light are uniformed distributed.

The correct option is B.