Alice and Bob are passengers in a high-speed train moving at a uniform speed of v = c/2. Alice is at the rear of the train car and Bob is at the front of the car. The length of the car measured in their frame is L'. Alice throws a ball to Bob at speed u' = c/3.
a) In the frame of the train, how long does it take the ball to reach Bob?
b) In the frame of the station, how long does it take the ball to reach Bob?
c) In the frame of the ball, how long does it take the ball to reach Bob?
d) Verify that the proper time between Alice throwing the ball and Bob receiving it is the same in all three frames.

it takes about 30 days for it to break down

speed of light in vacuum is 300,000 km/s

speed of light in other mediums is given by the expression v = c/n, where c is the speed of light in vacuum and n is the refractive index of medium.

for the first medium v = 200,000 km/s

  so, refractive index of medium = 300000/200000 = 1.5

    1.5 refractive index is usually for glass. so first medium is glass.

for the second medium v = 250,00 km/s

so, refractive index of medium = 300000/250000 = 1.2

    1.2 refractive index is usually for water. so second medium is water.

for the third medium v = 0 km/s

so, refractive index of medium = 300000/0 = ∞

    ∞ refractive index is usually for opaque mediums. so third medium is opaque medium.