To determine the potential energy of a [tex]\(25\text{ kg}\)[/tex] bicycle resting at the top of a [tex]\(3\text{ m}\)[/tex] high hill, we use the formula for gravitational potential energy:
[tex]\[ PE = mgh \][/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 ground.
Given data:
- Mass, [tex]\(m = 25\text{ kg}\)[/tex],
- Acceleration due to gravity, [tex]\(g = 9.81\text{ m/s}^2\)[/tex],
- Height, [tex]\(h = 3\text{ m}\)[/tex].
Step-by-step solution:
1. Identify the mass: [tex]\(m = 25\text{ kg}\)[/tex].
2. Identify the height: [tex]\(h = 3\text{ m}\)[/tex].
3. Use the standard value for acceleration due to gravity: [tex]\(g = 9.81\text{ m/s}^2\)[/tex].
4. Plug these values into the potential energy formula:
[tex]\[
PE = m \times g \times h
\][/tex]
So, substituting the given values:
[tex]\[
PE = 25\, \text{kg} \times 9.81\, \text{m/s}^2 \times 3\, \text{m}
\][/tex]
[tex]\[
PE = 735.75\, \text{J}
\][/tex]
Therefore, the potential energy of the bicycle is [tex]\(735.75 \text{ J}\)[/tex]. Considering the given choices:
- 75 J,
- 735 J,
- 245 J,
- 37.8 J,
The closest answer is [tex]\(735 \text{ J}\)[/tex].
So, the correct answer is:
[tex]\[ 735 \text{ J} \][/tex]
