Suppose the rest length of the box in figure is 30 light seconds. The train `T_1` travels at a speed of `0.8c`. Find the time elapsed between opening of `D_1` and `D_2` in the frame of `T_1`.

Explanation

The box moves in the frame of `T_1` with a speed of 0.8c so that
`gamma = 1 / (sqrt 1 - (0.8)^(2)) = 1 / 0.6`
In this frame, `D_2` opens after `D_1`. The time elapsed between the openings of the doors is
` Lv / C^2 gamma = (30 light seconds ) xx (0.8 c) / C^(2) xx 0.6 `
` (30 s ) C xx (0.8 c) / C^2 xx 0.6 = 40s`.