Mustadrak al-Hakim — Hadith 4054

It is narrated from Sayyidah Aishah (may Allah be pleased with her), the wife of the Prophet (peace and blessings be upon him), that the Messenger of Allah (peace and blessings be upon him) said: "If Allah Almighty had shown mercy to anyone of the people of Nuh, He would have shown mercy to the mother of the child." The Messenger of Allah (peace and blessings be upon him) said: "Nuh (peace be upon him) remained among his people for nine hundred and fifty years, calling them to Allah, until, when his last days came, he planted a tree which grew very large and spread in every direction. Then he cut it down and began making a ship from it. The people mocked him and said: 'He is making a ship on dry land; how will it sail?!' He would reply: 'You will soon come to know.' Then when he had finished it and the oven gushed forth, and the water increased in the streets, the mother of the child feared for him (her child), and she loved him with an intense love. So she went out towards the mountain until she reached a third of it. Then when the water reached her there, she went further up until she reached two thirds of the mountain. Then when the water reached her there too, she went further up until she climbed onto the top of the mountain. Then when the water reached her neck, she lifted the child up with her hand, until the water carried the child away as well. So if Allah Almighty had shown mercy to anyone of them, He would have shown mercy to the mother of the child."
The chain of this hadith is sahih (authentic), but the two Shaykhs did not record it.