Is "which was" / "that was" necessary?

[bawenang]

Greetings. I'm a new member in this forum. Nice to meet you all.

The reason I'm joining this forum is to ask about something that has bugged me for a while now. Which of these sentences is correct: "He was killed by a bus which was crossing over the road." or "He was killed by a bus crossing over the road." ? I was thinking that the second one is also correct but my friend said that only the first one is correct.

Thanks.

[Alan]

Both are grammatical but the first is absurd: it is presumably the pedestrian, and not the bus, that was doing the crossing...