A 4.00 bucket of water is accelerated upward by a cord of negligible mass whose breaking strength is 78.0 . If the bucket starts from rest, what is the minimum time required to raise the bucket a vertical distance of 10.0 without breaking the cord?

the above solution is correct except for the very last part. They did not take into account that it should have been:
t^2=(2h/a)
sqrt(t^2)=sqrt(2.06)
t=1.44

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