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?

Answer 1

ma=T-mg
a=(T/m)-g= 19.5 – 9.8 = 9.7 m/s²
h=at²/2=>
t=2h/a = 2•10/9.7 = 2.06 s.

Answer 2

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