Sure, let's solve this step-by-step.
To determine the potential energy (PE) of an object, we use the formula:
[tex]\[ PE = m \cdot g \cdot h \][/tex]
where:
- [tex]\( m \)[/tex] is the mass of the object,
- [tex]\( g \)[/tex] is the acceleration due to gravity,
- [tex]\( h \)[/tex] is the height above the reference point.
Given:
- The mass ([tex]\( m \)[/tex]) of the bicycle is 25 kg.
- The height ([tex]\( h \)[/tex]) of the hill is 3 meters.
- The standard acceleration due to gravity ([tex]\( g \)[/tex]) on Earth is approximately 9.81 m/s².
Now, substitute the given values into the formula:
[tex]\[ PE = 25 \, \text{kg} \times 9.81 \, \text{m/s}^2 \times 3 \, \text{m} \][/tex]
Upon performing the multiplication,
[tex]\[ PE = 735.75 \, \text{J} \][/tex]
Therefore, the potential energy of a 25 kg bicycle resting at the top of a hill 3 meters high is 735.75 Joules. The closest answer from the options provided is:
[tex]\[ \boxed{735 \, \text{J}} \][/tex]
