present participles, pronoun [duplicate]

Solution 1:

These are "nominate absolutes," and you may argue that they modify the entire clause to which they are attached or that they are "absolutely" free-standing.

In your example

The gas tank exploded, sending shrapnel through the air.

does the participle tell us what kind of tank it was, or does it tell us how the tank exploded? Neither seems quite right, since we need both a tank and an explosion to get shrapnel sent. So the entire clause seems a fair target of modification.

In the famous dangling constructions like,

The keys having been found, the car was driven home.

the finding doesn't seem to have much to do with either the type of car or the manner of its operation. So free-standing seems the better choice.