A $0\mathrm{.}28-$kg stone is held $1\mathrm{.}4$ m above the top edge of a water well and then dropped into it$.$ The well has a depth of $4\mathrm{.}7$ m$.$

$($a$)$ Relative to the configuration with the stone at the top edge of the well, what is the gravitational potential energy of the stone$$Earth system before the stone is released?

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$($b$)$ Relative to the configuration with the stone at the top edge of the well, what is the gravitational potential energy of the stone$$Earth system when it reaches the bottom of the well?

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$($c$)$ What is the change in gravitational potential energy of the system from release to reaching the bottom of the well?

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