To find the potential energy of a 25 kg bicycle resting at the top of a hill that is 3 meters high, we use the formula for gravitational potential energy, which is:
[tex]\[ PE = m \cdot g \cdot h \][/tex]
where:
- [tex]\( PE \)[/tex] is the potential energy
- [tex]\( m \)[/tex] is the mass of the object
- [tex]\( g \)[/tex] is the acceleration due to gravity
- [tex]\( h \)[/tex] is the height from which the object is located
Given:
- [tex]\( m = 25 \)[/tex] kg (the mass of the bicycle)
- [tex]\( g = 9.8 \)[/tex] m/s[tex]\(^2\)[/tex] (the standard acceleration due to gravity)
- [tex]\( h = 3 \)[/tex] m (the height of the hill)
By substituting these values into the formula, we get:
[tex]\[
PE = 25 \, \text{kg} \times 9.8 \, \text{m/s}^2 \times 3 \, \text{m}
\][/tex]
First, we calculate the product of the mass and gravity:
[tex]\[
25 \, \text{kg} \times 9.8 \, \text{m/s}^2 = 245 \, \text{N}
\][/tex]
Then, we multiply this result by the height:
[tex]\[
245 \, \text{N} \times 3 \, \text{m} = 735 \, \text{J}
\][/tex]
Therefore, the potential energy of the 25 kg bicycle resting at the top of a 3 meter high hill is:
[tex]\[
735 \, \text{J}
\][/tex]
So, the correct answer is:
[tex]\[
\boxed{735 \, \text{J}}
\][/tex]
