Answer :
Certainly! Let's work through this problem step-by-step.
First, we need to calculate the energy possessed by a stone with a mass of 10 kg when it's kept at a height of 5 meters. This energy is known as gravitational potential energy, and it can be calculated using the formula:
[tex]\[ \text{Energy} = m \times g \times h \][/tex]
Where:
- [tex]\( m \)[/tex] is the mass of the object,
- [tex]\( g \)[/tex] is the acceleration due to gravity (approximately [tex]\( 9.8 \, \text{m/s}^2 \)[/tex] on Earth),
- [tex]\( h \)[/tex] is the height above the ground.
For the stone:
- [tex]\( m = 10 \, \text{kg} \)[/tex]
- [tex]\( h = 5 \, \text{m} \)[/tex]
Plugging in the values, we get:
[tex]\[ \text{Energy} = 10 \times 9.8 \times 5 \][/tex]
[tex]\[ \text{Energy} = 490 \, \text{Joules} \][/tex]
So, the stone possesses 490 Joules of energy.
Next, we need to calculate how high a 40 kg boy could be raised using 19600 Joules of energy. We can use the same formula, rearranged to solve for height ([tex]\( h \)[/tex]):
[tex]\[ h = \frac{\text{Energy}}{m \times g} \][/tex]
For the boy:
- [tex]\( \text{Energy} = 19600 \, \text{Joules} \)[/tex]
- [tex]\( m = 40 \, \text{kg} \)[/tex]
Inserting these into the formula, we get:
[tex]\[ h = \frac{19600}{40 \times 9.8} \][/tex]
[tex]\[ h = \frac{19600}{392} \][/tex]
[tex]\[ h = 50 \, \text{meters} \][/tex]
Therefore, the boy could be raised to a height of 50 meters above the ground with 19600 Joules of energy.
First, we need to calculate the energy possessed by a stone with a mass of 10 kg when it's kept at a height of 5 meters. This energy is known as gravitational potential energy, and it can be calculated using the formula:
[tex]\[ \text{Energy} = m \times g \times h \][/tex]
Where:
- [tex]\( m \)[/tex] is the mass of the object,
- [tex]\( g \)[/tex] is the acceleration due to gravity (approximately [tex]\( 9.8 \, \text{m/s}^2 \)[/tex] on Earth),
- [tex]\( h \)[/tex] is the height above the ground.
For the stone:
- [tex]\( m = 10 \, \text{kg} \)[/tex]
- [tex]\( h = 5 \, \text{m} \)[/tex]
Plugging in the values, we get:
[tex]\[ \text{Energy} = 10 \times 9.8 \times 5 \][/tex]
[tex]\[ \text{Energy} = 490 \, \text{Joules} \][/tex]
So, the stone possesses 490 Joules of energy.
Next, we need to calculate how high a 40 kg boy could be raised using 19600 Joules of energy. We can use the same formula, rearranged to solve for height ([tex]\( h \)[/tex]):
[tex]\[ h = \frac{\text{Energy}}{m \times g} \][/tex]
For the boy:
- [tex]\( \text{Energy} = 19600 \, \text{Joules} \)[/tex]
- [tex]\( m = 40 \, \text{kg} \)[/tex]
Inserting these into the formula, we get:
[tex]\[ h = \frac{19600}{40 \times 9.8} \][/tex]
[tex]\[ h = \frac{19600}{392} \][/tex]
[tex]\[ h = 50 \, \text{meters} \][/tex]
Therefore, the boy could be raised to a height of 50 meters above the ground with 19600 Joules of energy.
