How to calculate the minimum energy to get things out of a gravitation field?

1) a) What is the gravitational potential energy of a 60kg student on the surface of the earth?

my answer: 3.75 x 10^9 Jkg^-1

b) What then, is the minimum energy that would be required to get this student completely out of the earth's gravitation field?

is there an equation to calculate this? or do you just calculate the answer for a by the mass of the student?

What is the definition of potential energy?

1) a) What is the gravitational potential energy of a 60kg student on the surface of the earth?

my answer: 3.75 x 10^9 Jkg^-1

b) What then, is the minimum energy that would be required to get this student completely out of the earth's gravitation field?

is there an equation to calculate this? or do you just calculate the answer for a by the mass of the student?

for (a) it's not asking for the potential, it's asking for potential energy. Although you're magnitude seems right... units are wrong though which suggests you're using the wrong eq.

(b) I meant specifically what is the definition of gravitational potential energy?

im using the right equation... i just got confused... the units are suppose to be joules and youre right jkg^-1 is for potential.

Gravitational potential energy is energy an object possesses because of its position on a gravitational field

The answer is correct and the unit is joule.
However it should be negative.
This is due to the (correct) definition of gravitational potential energy.
This definition will tell you directly the answer to part b

how am i suppose to answer it if i dont know the distance of earth's gravitational field?

There is no "distance of earth's gravitational field" as such.
You assume, for this calculation that "completely" means, that you have moved the object to a point so far away that the gravitational force is zero.
Where's that?
How does this relate to the potential energy?

would it be 2.25 x 10^11 J

You still haven't got the correct definition of gravitational potential energy.

The definition is:
The gravitational potential energy of a mass m at a point in a field is defined as the amount of work done bringing the mass from infinity to that point.
In addition, the value of potential energy is defined as zero at infinity.

Infinity because the field is zero only at that point (where the force is also zero.)

Now because gravitational fields are always attractive, you don't do work to move the object from infinity to a point, the field does the work. (The force is attractive.)
In fact, you have to do work to move the object from some place in the field to infinity. (Out of the field completely.)

For this reason, objects in a gravitational field have negative potential energy.
Why?
Because if I have to do, say, 1000J of work to move you to infinity where your potential energy is zero, you will gain 1000J of energy and it will become zero. The way this works is that you started with -1000J of potential energy, were given 1000J, and now have zero.

Can you answer the 2nd part now, as you have correctly calculated, but missing out the minus sign, the potential energy at the earth's surface.

have I got the right answer for the second part or the first part? which one is missing the minus sign?

The numerical answer for part 1 is correct, missing the minus sign, and the unit is joule.

so if you want to escape the the gravitational field (you would escape at 0)
then this means that you do -3.75 x 10^9 - (-3.75 x 10^9) cause that way the gravitational potential energy would then = 0
which would mean the gravitational field is not acting on you anymore
is that right?

If the potential energy is - 3.75x10⁹J at the Earth's surface you need to give it +3.75x10⁹J to get it to infinity where it is completely out of the Earth's gravitational field and has zero potential energy.

in the calculation the (- 3.75 x 10^9) turns into a + so isnt that the same?