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Answer :
To determine the height from which the boulder rolled down, we need to use the concept of gravitational potential energy. The formula for gravitational potential energy is:
[tex]\[ \text{Potential Energy (PE)} = m \cdot g \cdot h \][/tex]
Where:
- [tex]\( m \)[/tex] is the mass of the object (in kilograms),
- [tex]\( g \)[/tex] is the acceleration due to gravity (approximately [tex]\( 9.81 \, \text{m/s}^2 \)[/tex] on Earth),
- [tex]\( h \)[/tex] is the height (in meters).
From the problem, we know:
- The mass [tex]\( m \)[/tex] of the boulder is [tex]\( 145 \, \text{kg} \)[/tex].
- The energy is [tex]\( 30 \, \text{kJ} \)[/tex], which we need to convert to joules since 1 kJ = 1000 J. So, [tex]\( 30 \, \text{kJ} = 30,000 \, \text{J} \)[/tex].
We are given the potential energy (30,000 J) and need to find the height ([tex]\( h \)[/tex]). Rearrange the formula to solve for height:
[tex]\[ h = \frac{\text{PE}}{m \cdot g} \][/tex]
Substitute the known values into the equation:
[tex]\[ h = \frac{30,000 \, \text{J}}{145 \, \text{kg} \times 9.81 \, \text{m/s}^2} \][/tex]
Now, calculate:
[tex]\[ h \approx \frac{30,000}{145 \times 9.81} \][/tex]
[tex]\[ h \approx \frac{30,000}{1421.85} \][/tex]
[tex]\[ h \approx 21.09 \, \text{meters} \][/tex]
Thus, the boulder was approximately 21.09 meters high.
[tex]\[ \text{Potential Energy (PE)} = m \cdot g \cdot h \][/tex]
Where:
- [tex]\( m \)[/tex] is the mass of the object (in kilograms),
- [tex]\( g \)[/tex] is the acceleration due to gravity (approximately [tex]\( 9.81 \, \text{m/s}^2 \)[/tex] on Earth),
- [tex]\( h \)[/tex] is the height (in meters).
From the problem, we know:
- The mass [tex]\( m \)[/tex] of the boulder is [tex]\( 145 \, \text{kg} \)[/tex].
- The energy is [tex]\( 30 \, \text{kJ} \)[/tex], which we need to convert to joules since 1 kJ = 1000 J. So, [tex]\( 30 \, \text{kJ} = 30,000 \, \text{J} \)[/tex].
We are given the potential energy (30,000 J) and need to find the height ([tex]\( h \)[/tex]). Rearrange the formula to solve for height:
[tex]\[ h = \frac{\text{PE}}{m \cdot g} \][/tex]
Substitute the known values into the equation:
[tex]\[ h = \frac{30,000 \, \text{J}}{145 \, \text{kg} \times 9.81 \, \text{m/s}^2} \][/tex]
Now, calculate:
[tex]\[ h \approx \frac{30,000}{145 \times 9.81} \][/tex]
[tex]\[ h \approx \frac{30,000}{1421.85} \][/tex]
[tex]\[ h \approx 21.09 \, \text{meters} \][/tex]
Thus, the boulder was approximately 21.09 meters high.
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