To calculate the gravitational potential energy (GPE) of a 2 kg bottle of soda falling off a kitchen table that is 0.76 m tall, you need to use the formula for gravitational potential energy:
[tex]\[ \text{GPE} = m \cdot g \cdot h \][/tex]
where:
- [tex]\( m \)[/tex] is the mass (in kilograms)
- [tex]\( g \)[/tex] is the acceleration due to gravity (in meters per second squared)
- [tex]\( h \)[/tex] is the height (in meters)
In this problem:
- The mass [tex]\( m \)[/tex] is 2 kg.
- The height [tex]\( h \)[/tex] is 0.76 meters.
- The acceleration due to gravity [tex]\( g \)[/tex] is typically approximated as 9.8 m/s² near the Earth's surface (despite the text's small typographical error in units for gravity).
Substituting these values into the formula gives:
[tex]\[ \text{GPE} = (2 \, \text{kg}) \times (9.8 \, \text{m/s}^2) \times (0.76 \, \text{m}) \][/tex]
Calculating this, you get:
[tex]\[ \text{GPE} = 2 \times 9.8 \times 0.76 \][/tex]
Carefully computing the multiplication:
[tex]\[ 2 \times 9.8 = 19.6 \][/tex]
[tex]\[ 19.6 \times 0.76 = 14.896 \][/tex]
Therefore, the gravitational potential energy (GPE) is 14.896 Joules.
Now, let's match this solution to the correct multiple-choice answer. The correct formula to use here is:
[tex]\[ (2) (0.76) (9.8) \][/tex]
Which corresponds to option C:
[tex]\[ (2)(0.76) 9.8 \][/tex]
Thus, the correct answer is:
C. [tex]\((2)(0.76) 9.8\)[/tex]
