A ball of mass 0.10 kg is located 1.81 m above the surface of the ground. It is

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For a vertical displacement y, the work done by gravity is W = -m gy, so W = -.10 kg * g * -1.81 m = .000181 m kg^2 The speed of the ball is given by conservation of energy; original energy is given by m g h. This is all converted to kinetic energy, of the form  1/2 m v^2. So 1/2 m v^2 = m g h, and so v=(2 g h)= 5.958 m/s This would give v=14.30 m/s = (2 g h), so h = (14.30 m/s)^2/ (2 g) = 102245 m

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