Lifeguards spotted the 4-foot predator and urged everyone to come onto land about one minute after Plemmons had snapped a photo of her family in the water, her mother, Susan Bare, told the Sun News.
"We turned right then and saw it. I'm talking a foot from us," Bare said.
In Plemmons' video, a woman can be heard shouting, "What is it? What is it? What is that? Baby shark?" as another jokes, "Go get it!"
After getting the all-clear, the family ventured out into the waves again.
"This is the closest I've ever seen, and you can tell by the video," Bare told the Sun News.
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