Answer :
To determine the height from which the object was dropped, we can use the concept of energy conservation. Here’s a step-by-step explanation:
1. Understanding Energy Conservation: When an object is dropped from a height, its potential energy is converted into kinetic energy as it falls. Initially, at the top, all the energy is potential energy, and right before it hits the ground, this energy becomes kinetic energy.
2. Formula for Potential Energy (PE):
[tex]\[
\text{PE} = m \cdot g \cdot h
\][/tex]
where:
- [tex]\( m \)[/tex] is the mass (in kg),
- [tex]\( g \)[/tex] is the acceleration due to gravity (approximately 9.81 m/s²),
- [tex]\( h \)[/tex] is the height (in meters).
3. Formula for Kinetic Energy (KE):
[tex]\[
\text{KE} = \frac{1}{2} \cdot m \cdot v^2
\][/tex]
where:
- [tex]\( v \)[/tex] is the velocity (in m/s).
4. Given Data:
- Mass ([tex]\( m \)[/tex]) = 14 kg,
- Kinetic Energy ([tex]\( \text{KE} \)[/tex]) = 2112 J.
5. Determine the Height:
Since all potential energy (PE) is converted to kinetic energy (KE) as the object hits the ground, we have:
[tex]\[
m \cdot g \cdot h = \text{KE}
\][/tex]
Solving for height ([tex]\( h \)[/tex]):
[tex]\[
h = \frac{\text{KE}}{m \cdot g}
\][/tex]
Substitute the given values:
[tex]\[
h = \frac{2112 \, \text{J}}{14 \, \text{kg} \cdot 9.81 \, \text{m/s}^2}
\][/tex]
6. Calculate:
[tex]\[
h \approx \frac{2112}{137.34} \approx 15.38 \, \text{meters}
\][/tex]
Therefore, the object was dropped from a height of approximately 15.38 meters.
1. Understanding Energy Conservation: When an object is dropped from a height, its potential energy is converted into kinetic energy as it falls. Initially, at the top, all the energy is potential energy, and right before it hits the ground, this energy becomes kinetic energy.
2. Formula for Potential Energy (PE):
[tex]\[
\text{PE} = m \cdot g \cdot h
\][/tex]
where:
- [tex]\( m \)[/tex] is the mass (in kg),
- [tex]\( g \)[/tex] is the acceleration due to gravity (approximately 9.81 m/s²),
- [tex]\( h \)[/tex] is the height (in meters).
3. Formula for Kinetic Energy (KE):
[tex]\[
\text{KE} = \frac{1}{2} \cdot m \cdot v^2
\][/tex]
where:
- [tex]\( v \)[/tex] is the velocity (in m/s).
4. Given Data:
- Mass ([tex]\( m \)[/tex]) = 14 kg,
- Kinetic Energy ([tex]\( \text{KE} \)[/tex]) = 2112 J.
5. Determine the Height:
Since all potential energy (PE) is converted to kinetic energy (KE) as the object hits the ground, we have:
[tex]\[
m \cdot g \cdot h = \text{KE}
\][/tex]
Solving for height ([tex]\( h \)[/tex]):
[tex]\[
h = \frac{\text{KE}}{m \cdot g}
\][/tex]
Substitute the given values:
[tex]\[
h = \frac{2112 \, \text{J}}{14 \, \text{kg} \cdot 9.81 \, \text{m/s}^2}
\][/tex]
6. Calculate:
[tex]\[
h \approx \frac{2112}{137.34} \approx 15.38 \, \text{meters}
\][/tex]
Therefore, the object was dropped from a height of approximately 15.38 meters.
