The total energy of the object at the height h is its potential energy, which is
mgh. At this point, the kinetic energy is zero, so the total energy is entirely due to its potential energy.
What is the total energy of the object at the height ℎ?
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At height ℎ, the total energy of the object is the sum of its potential and kinetic energies. Since the object is initially at rest, its total energy is purely potential, given by mgh, where m is mass and g is gravity.