What would happen if I shot a near-light-speed bullet at the moon? What would happen if I shot a bullet at 90% of light speed from earth to the moon? Would it make it through the atmosphere? Would it have any negative effects on the earth's atmosphere as it passes through it? What would happen to the moon? Would the man who shot the bullet even survive?
So my question is what would happen if you shot a near-light-speed bullet at the moon?
 A: The kinetic energy of such a bullet is around $3 \times 10^{15}$ J (I took a 30 gram bullet; the kinetic energy is given by $(\gamma-1) m c^2$ where $\gamma = (1-v^2/c^2)^{-1/2} \simeq 2.29$.) This is of the order of the energy in an explosion of one million tonnes of TNT. The largest power station in the world can produce 22 GW of power. It would take this power station about 3 days to provide the required energy for your bullet. So either you will need to use a much lighter bullet, or you will have to wait before firing it, or you will have to try to harness the power of a huge explosion.
Next, how to accelerate the bullet? I suppose a rail gun or some sort of electromagnetic method would be best, but I can't see how to do it. The bullet will deform into pancake shape or maybe melt. But if we suppose it somehow got launched on its journey, it will then encounter the air. On its journey upwards it bores out a cylindrical hole through the atmosphere, encountering about 100 grams of air in about $0.1$ milliseconds. So this is like a collision. The bullet will not survive this collision with the air, I think. I think it will flatten, heat up, and spray apart into a sort of splat.
However, maybe somehow there can be a material or a shape which can survive, or we imagine some sort of double-bullet with the first one carving out a passage for the second. Well in this case the surviving bullet will easily make it to the moon. If will then hit the moon with its kinetic energy almost undiminished (the change in gravitational potential energy is negligible compared to the kinetic energy of the bullet). So it will then cause a megaton explosion on the moon, producing a moonquake and a lot of dust and leaving an impact crater.
