Check if where is the potential energy at the drop point and with the ground as zero. Assuming my understanding of impact velocity in this question is correct.
Just plug in the values of the variables into the inequality and see if it holds.
(height)
(velocity)
(standard gravity)
so you can just divide it out.
so it will not burst.
This is not exactly an answer to a calculus question, so I don't think I have interpreted the impact velocity correctly.