The height in which the kinetic energy of the rock is twice the potential energy is 7 m.
The given parameters;
The potential energy of the rock at the given height is calculated as;
P.E = mgh
P.E = 8 x 9.8 x 21
P.E = 1646.4 J
The is the total initial mechanical energy of the rock.
Let the height in which the kinetic energy equals 2 potential energy = h
Apply the principle of conservation of mechanical energy;
Total final mechanical energy = Total initial mechanical energy
[tex]P.E + K.E = M.A\\\\P.E + 2P.E = M.A\\\\3P.E = M.A\\\\3(mgh) = M.A\\\\h(3mg) = M.A\\\\h(3 \times 8 \times 9.8)= 1646.4\\\\235.2h =1646.4\\\\h = \frac{1646.4}{235.2} \\\\h = 7 \ m[/tex]
Thus, the height in which the kinetic energy of the rock is twice the potential energy is 7 m.
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