Answer :
Sure, let's calculate the potential energy of the bicycle step-by-step.
### Given:
- Mass of the bicycle, [tex]\( m = 25 \)[/tex] kg.
- Height of the hill, [tex]\( h = 3 \)[/tex] meters.
- Acceleration due to gravity, [tex]\( g = 9.8 \)[/tex] m/s².
### Formula:
The potential energy (PE) can be calculated using the formula:
[tex]\[ PE = m \times g \times h \][/tex]
### Step-by-Step Calculation:
1. Identify the mass (m):
The mass of the bicycle is 25 kg.
2. Identify the height (h):
The height of the hill is 3 meters.
3. Identify the acceleration due to gravity (g):
The acceleration due to gravity is 9.8 m/s².
4. Substitute these values into the formula:
[tex]\[
PE = 25 \, \text{kg} \times 9.8 \, \text{m/s}^2 \times 3 \, \text{m}
\][/tex]
5. Perform the multiplication:
[tex]\[
PE = 25 \times 9.8 \times 3
\][/tex]
6. Calculate the result:
[tex]\[
PE = 735 \, \text{J}
\][/tex]
Therefore, the potential energy of the 25 kg bicycle resting at the top of a 3-meter high hill is 735 J.
So, the correct answer is:
735 J.
### Given:
- Mass of the bicycle, [tex]\( m = 25 \)[/tex] kg.
- Height of the hill, [tex]\( h = 3 \)[/tex] meters.
- Acceleration due to gravity, [tex]\( g = 9.8 \)[/tex] m/s².
### Formula:
The potential energy (PE) can be calculated using the formula:
[tex]\[ PE = m \times g \times h \][/tex]
### Step-by-Step Calculation:
1. Identify the mass (m):
The mass of the bicycle is 25 kg.
2. Identify the height (h):
The height of the hill is 3 meters.
3. Identify the acceleration due to gravity (g):
The acceleration due to gravity is 9.8 m/s².
4. Substitute these values into the formula:
[tex]\[
PE = 25 \, \text{kg} \times 9.8 \, \text{m/s}^2 \times 3 \, \text{m}
\][/tex]
5. Perform the multiplication:
[tex]\[
PE = 25 \times 9.8 \times 3
\][/tex]
6. Calculate the result:
[tex]\[
PE = 735 \, \text{J}
\][/tex]
Therefore, the potential energy of the 25 kg bicycle resting at the top of a 3-meter high hill is 735 J.
So, the correct answer is:
735 J.
