To find the sled's potential energy, we can use the formula for gravitational potential energy:
[tex]\[ PE = mgh \][/tex]
Where:
- [tex]\( PE \)[/tex] is the potential energy
- [tex]\( m \)[/tex] is the mass of the sled
- [tex]\( g \)[/tex] is the acceleration due to gravity
- [tex]\( h \)[/tex] is the height
Given:
- Mass ([tex]\( m \)[/tex]) = 45 kg
- Acceleration due to gravity ([tex]\( g \)[/tex]) = 9.8 m/s²
- Height ([tex]\( h \)[/tex]) = 2 m
Now, we can plug in the given values into the formula:
[tex]\[ PE = 45 \, \text{kg} \times 9.8 \, \text{m/s}^2 \times 2 \, \text{m} \][/tex]
First, calculate the product of the mass and the acceleration due to gravity:
[tex]\[ 45 \, \text{kg} \times 9.8 \, \text{m/s}^2 = 441 \, \text{N} \][/tex]
Then, multiply this result by the height:
[tex]\[ 441 \, \text{N} \times 2 \, \text{m} = 882 \, \text{J} \][/tex]
So, the sled's potential energy at the top of the slope is:
[tex]\[ 882 \, \text{J} \][/tex]
Therefore, the correct answer is:
[tex]\[ 882 \, \text{J} \][/tex]
