A mother has described to an inquest how she saw her five-year-old daughter hit by a “freak wave” that swept her out to sea where she drowned.

Rose Carter was walking along the beach at Durdle Door in Dorset with her sister and her mother on 18 April when she was hit by the “eight-foot wave”, Bournemouth coroner’s court heard on Wednesday.

The coastguard was alerted and a military vessel helped rescue Rose, but she was pronounced dead at Dorset county hospital in Dorchester.

Her mother, Sofia Carter, from Salisbury in Wiltshire, said in a statement to the court that she was also submerged by the waves as she tried to save her daughter.

“I saw a really big wave that went over her head and knocked her off her feet,” she said, adding that she herself was knocked into the water by a second wave. “When I stood up I could no longer see Rose.”

A bystander called 999 and a Ministry of Defence boat arrived within minutes, but Rose was already beyond the breaking waves by then.

“A man with binoculars directed the boat to where Rose was,” Carter said. “Rose was taken from the sea.” She told the hearing that although the sea was rough she did not think it was dangerous as they walked along the edge of the beach with Rose about 10ft behind her.

“Rose was a strong child and happy in the water and was able to swim with doggy paddle and had previously swam lengths,” she said.

A witness said she went into the water in an attempt to rescue Rose but was swept back to the beach by the waves, fracturing one of her ribs in the process.

“I saw Rose had been knocked flat by the waves and was being pulled in by the riptide and was half or three-quarters of the way down the beach and that was within a second,” Lucy Seviour, a former triathlete, said. “I could see Rose for half a second and she was only half a metre away but I tried to move and was washed up on the beach.”

She said she then tried to stop Carter from going into the water. “Obviously it’s her kid so she went straight back in,” she said.

Another witness, Gordon Cobb, said that the wave was eight-foot high and that attempts to save Rose were futile. “I could see a little girl’s head sticking out of the wave, physically there was no way she could have got through the wave,” he said. “I had to watch her drift out to sea.

“The sea was very dangerous that day and the wave that hit the girl was a freak wave and came out of the blue, and no other wave was like it before.”

The coroner, Brendan Allen, ruled her death by drowning was accidental. “Tragically, Rose and her family were walking along the beach at the same time the freak wave crashed up the beach and washed Rose off her feet,” he said, going on to commend Seviour for her “selfless” rescue efforts.

“It’s not something that could have been foreseen by anyone, it’s a tragedy that this has happened in these circumstances.”