Physically vulnerable: The cyclist wasn't wearing a helmet when he crashed, making himself vulnerable to severe injury.
Physically fragile: The elderly woman was too fragile to be riding the bike.
Emotionally vulnerable: The leader admitted to his team that he made a mistake, and wanted to hear feedback about how he could have avoided the mistake. In doing so, he made himself vulnerable to hear things that he may not like.
Emotionally fragile: The teenager is very sensitive about her appearance, she is too fragile to take any advice on the matter.