A delicious lime weighing $22\mathrm{.}9$ grams falls off Prof. P$.\text{'}$s dwarf lime tree that he has now dragged outside, falling $87$ cm and burrows $21\mathrm{.}7$ mm into the ground.$$ What is the average force in Newtons between the ground and the lime as it sinks$?$

$($solve using energy considerations, and don't forget $5$N will bruise that lime$!)$