37 seconds is a long time
In one of the film’s initial scenes, Rose gets convinced to jump off the ledge by Jack—just as she falls and is left hanging over the sea with just Jack for support. It’s not as easy as it might seem to hold up someone for 37 seconds, so in practice, Rose would most likely wind up in deep trouble.
Being a wealthy woman in the 1910s, she was probably not into hard labor. Her attire would have made things more difficult, and the fact that she was hanging would have made it nearly impossible to hold on to her for that long. What exactly would the movie be about if she passed away at that point?