Let's analyze the situation step by step to determine the correct answer.
1. Understanding Potential Energy: The gravitational potential energy ([tex]\(PE\)[/tex]) of an object is given by the formula:
[tex]\[
PE = mgh
\][/tex]
where:
- [tex]\(m\)[/tex] is the mass of the object
- [tex]\(g\)[/tex] is the acceleration due to gravity (approximately [tex]\(9.8 \, \text{m/s}^2\)[/tex])
- [tex]\(h\)[/tex] is the height above the ground
2. Initial Potential Energy: Assume the parcel has a certain mass [tex]\(m\)[/tex] and it was lifted to an initial height [tex]\(h\)[/tex].
[tex]\[
PE_{\text{initial}} = mgh
\][/tex]
3. Final Potential Energy: Now, if the parcel is lifted to twice the initial height ([tex]\(2h\)[/tex]), the potential energy becomes:
[tex]\[
PE_{\text{final}} = mg(2h) = 2mgh
\][/tex]
4. Ratio of Final to Initial Potential Energy: To find how many times the final potential energy is compared to the initial potential energy, we divide [tex]\(PE_{\text{final}}\)[/tex] by [tex]\(PE_{\text{initial}}\)[/tex]:
[tex]\[
\text{Ratio} = \frac{PE_{\text{final}}}{PE_{\text{initial}}} = \frac{2mgh}{mgh} = 2
\][/tex]
This tells us that if Joseph lifts the parcel twice as high, the potential energy of the parcel will be twice its initial potential energy.
Thus, the correct option is:
- Twice its potential energy
