A javelin of length $2 \mathrm{~m}$ is thrown horizontally and lengthwise into a shed of length $1.5 \mathrm{~m}$ at a speed of $0.8 c$, where $c$ is the speed of light.

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

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

(c) Draw a space-time diagram in the rest frame coordinates $(c t, x)$ of the shed, showing the world lines of both ends of the javelin, and of the front and back of the shed. 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 shed.

(d) Clearly mark the space-time events corresponding to (A) the trailing end of the javelin entering the shed, and (B) the leading end of the javelin hitting the back of the shed. Give the corresponding $(c t, x)$ and $\left(c t^{\prime}, x^{\prime}\right)$ coordinates for both (A) and (B). Are these two events space-like, null or time-like separated? How does the javelin fit inside the shed, even though it is initially longer than the shed in its own rest frame?