Let "h" be the height of the tree. Then the total energy of the apple at the top of the tree will be eaual to it's potential energy:
"E_1 = W = mgh"
where "m = 0.1 kg" is the mass of the apple and "g = 9.8m\/s^2" is the free-fall acceleration due to gravity.
At the point 2.0 m above the ground the energy of the apple will be the sum of the kinetic and potential energies:
"E_2 = mv^2\/2 + mg\\cdot 2"
where "v = 10m\/s" is the speed of the apple at that point.
According to the conservation energy law:
"E_1 = E_2""mgh = mv^2\/2 + mg\\cdot 2\\\\\nh = v^2\/2 + 2g = 10^2\/2 + 2\\cdot 9.8 = 69.6 m"
Answer. h = 69.6 m.