(a) The gravitational potential energy of the stone before it is released is:
[tex]U=mg \Delta h[/tex]
where m=0.30 kg is the mass of the stone, [tex]g=9.81 m/s^2[/tex] and [tex]\Delta h[/tex] is the difference in height relative to the reference level, which is the top edge of the well. Therefore, since the stone in this situation is at h=1.2 m above the top edge of the well, [tex]\Delta h=1.2 m[/tex], and the gravitational potential energy is
[tex]U=(0.30 kg)(9.81 m/s^2)(1.2 m)=3.5 J[/tex]
(b) Similarly, the gravitational potential energy when the stone reaches the bottom of the well is
[tex]U=mg \Delta h[/tex]
but this time the stone is at the bottom of the well, so at 5.1 m below the top edge of the well, therefore [tex]\Delta h=-5.1 m[/tex]. So, the gravitational potential energy in this situation is
[tex]U=(0.30 kg)(9.81 m/s^2)(-5.1 m)=-15.0 J[/tex]
(c) The change in gravitational potential energy from release to the bottom of the well is:
[tex]\Delta U= U_b-U_a=-15.0 J-(3.5 J)=-18.5 J[/tex]
