Answer:
Twice
Explanation:
Potential energy is directly proportional to the mass of the object, height and acceleration of gravity, given by the general expression [tex]E_p = mgh[/tex], where m is mass, g is acceleration of gravity and h is height.
Assume that initially [tex]E_{p_1} = mgh_1[/tex]. The mass of this object, as well as the acceleration of gravity, don't change. The only variable that changes is height, so the final potential energy would be [tex]E_{p_2} = mgh_2[/tex].
We know that [tex]h_2 = 2h_1[/tex], so we will find the ratio of the two potential energy values:
[tex]\dfrac{E_{p_2}}{E_{p_1}} = \dfrac{mgh_2}{mgh_1} = \dfrac{h_2}{h_1} = 2[/tex]
Therefore, since height increases twice, the potential energy also increases twice.
