A javelin of length 4 metres is thrown at a speed of $\frac{12}{13} c$ horizontally and lengthwise through a barn of length 3 metres, which is open at both ends. (Here $c$ denotes the speed of light.)

(a) What is the length of the javelin in the rest frame of the barn?

(b) What is the length of the barn in the rest frame of the javelin?

(c) Define the rest frame coordinates of the barn and of the javelin such that the point where the trailing end of the javelin enters the barn is the origin in both frames. Draw a space-time diagram in the rest frame coordinates $(c t, x)$ of the barn, showing the world lines of both ends of the javelin and of the front and back of the barn. Draw a second space-time diagram in the rest frame coordinates $\left(c t^{\prime}, x^{\prime}\right)$ of the javelin, again showing the world lines of both ends of the javelin and of the front and back of the barn.

(d) Clearly mark the space-time events corresponding to (A) the trailing end of the javelin entering the barn, and (B) the leading end of the javelin exiting the back of the barn. Give the corresponding $(c t, x)$ and $\left(c t^{\prime}, x^{\prime}\right)$ coordinates for (B).

Are the events (A) and (B) space-like, null, or time-like separated?

As the javelin is longer than the barn in one frame and shorter than the barn in another, it might be argued that the javelin is contained entirely within the barn for a period according to an observer in one frame, but not according to an observer in another. Explain how this apparent inconsistency is resolved.