Does an object travelling at the speed of light cast a shadow? Asked by my 8yo today and left me scratching my head.
 A: Whenever you run into a "can't go there" question, the next best thing is to see what happens when you approach the limit.
So let's imagine an object traveling at 0.999...c . If the sun is overhead, and we look for a shadow below it, will there be a shadow?
Let's slow everything down. The photons of the sun are now falling with the speed of raindrops, and our rocket is traveling at the speed of the rain drops. The front of the rocket will get very wet, and a "cylinder" of dry air will follow behind it. If you are standing below the rocket, it will briefly stop raining as it passes overhead.
So yes, there will be a shadow.
Afterthought:
Obviously if the object is traveling towards me "at the speed of light", it intercepts very few photons (at the limit of the speed of light it will never hit any) and will in essence have no shadow (although it will seem the lights go out when it reaches us...); and when it travels towards the light it will cast a "normal" shadow.
A: First of all, no object can travel the speed of light if it has any mass at all. If an object travels, say 99,999999% the speed of light, than yes, it will cast a shadow, since the speed of light is the same in all reference frames. 
Edit: you should watch this video, it covers a lot of related questions: http://m.youtube.com/watch?v=JTvcpdfGUtQ
