Crews responded to Castle Park amusement park on the 3500 block of Polk Street at about 4:37 p.m.
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The patients, family members, were transferred to a local hospital.
Two of the patients, including a 10-year-old boy, had minor injuries, officials said. One other woman was severely injured when she was ejected from the ride.
Video showed the injured boy and the man moments after the log carrying them flipped over.
Fire department officials said there was a mechanical failure of the ride's water pump.
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The ride was closed and an investigation by Division of Occupational Safety and Health was undertaken for the park. The rest of the amusement park remained opened.
Riverside Fire said no patients were trapped when the incident occurred.
Some families visiting the park said they're surprised by the accident.
"I've been coming here since I was a kid and never seen this happen," Omar Ramirez said. "This is the first time I've seen this happen."
Officials said the cause of the accident will be investigated by the California Department of Health and Safety.