Looks like a classic use of F = ma

The mass is given in the problem as 25.0 kg.

The acceleration you can find quickly if you know that the acceleration of gravity ("g") = 9.81 m/s^{2}. This makes the gymnast's acceleration = 68.67 m/s^{2}

Now we can just plug back in:

F = (25.0kg) * (68.67 m/s^{2})

F = 1716.75 N downwards

Keeping the 3 significant digits, the most appropriate answer would be __F = 1720 N downwards__

NOTES:

1) Remember that force is a vector, so your answer needs to have a magnitude (aka a number) and a direction. If you don't need a direction, the question will usually say "find the magnitude".

2) The force from the ground is equal an opposite to your answer, so 1720 N upwards.

3) Significant figures: You can google the rules, but the general idea is to be as precise as the given data. So, don't write your answers to 5 decimal points and don't round more than necessary.