The altitude or height of the pole vaulter as she crosses the bar is 4.04 m.
The height of the pole vaulter is determined from the change in kinetic energy which is equal to the potential energy at that height.
h = (v - u)²/2g
h = (10 - 1.1)²/2 * 9.8
h = 4.04 m.
In conclusion, the height is determined from the potential energy at that height.
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