Answer :
To determine the total mechanical energy of the paper airplane flying above the ground, we need to consider both its potential energy and kinetic energy.
1. Calculating Potential Energy (PE)
- The formula for potential energy is given by:
[tex]\[ PE = m \times g \times h \][/tex]
where:
- [tex]\( m \)[/tex] is the mass of the object (0.1 kg in this case),
- [tex]\( g \)[/tex] is the acceleration due to gravity (approximately 9.8 m/s²),
- [tex]\( h \)[/tex] is the height above the ground (1.5 m).
Substituting the given values:
[tex]\[ PE = 0.1 \times 9.8 \times 1.5 = 1.47 \, \text{J} \][/tex]
2. Calculating Kinetic Energy (KE)
- The formula for kinetic energy is:
[tex]\[ KE = \frac{1}{2} \times m \times v^2 \][/tex]
where:
- [tex]\( m \)[/tex] is the mass of the object (0.1 kg),
- [tex]\( v \)[/tex] is its velocity (2 m/s).
Substituting the given values:
[tex]\[ KE = \frac{1}{2} \times 0.1 \times (2^2) = \frac{1}{2} \times 0.1 \times 4 = 0.2 \, \text{J} \][/tex]
3. Calculating Total Mechanical Energy (TME)
- The total mechanical energy is the sum of potential and kinetic energies:
[tex]\[ TME = PE + KE \][/tex]
Substituting the computed values of potential and kinetic energy:
[tex]\[ TME = 1.47 \, \text{J} + 0.2 \, \text{J} = 1.67 \, \text{J} \][/tex]
Thus, the total mechanical energy of the paper airplane is [tex]\( \boxed{1.67 \, \text{J}} \)[/tex]. So, the correct answer is:
[tex]\[ \boxed{B. \, 1.67 J} \][/tex]
1. Calculating Potential Energy (PE)
- The formula for potential energy is given by:
[tex]\[ PE = m \times g \times h \][/tex]
where:
- [tex]\( m \)[/tex] is the mass of the object (0.1 kg in this case),
- [tex]\( g \)[/tex] is the acceleration due to gravity (approximately 9.8 m/s²),
- [tex]\( h \)[/tex] is the height above the ground (1.5 m).
Substituting the given values:
[tex]\[ PE = 0.1 \times 9.8 \times 1.5 = 1.47 \, \text{J} \][/tex]
2. Calculating Kinetic Energy (KE)
- The formula for kinetic energy is:
[tex]\[ KE = \frac{1}{2} \times m \times v^2 \][/tex]
where:
- [tex]\( m \)[/tex] is the mass of the object (0.1 kg),
- [tex]\( v \)[/tex] is its velocity (2 m/s).
Substituting the given values:
[tex]\[ KE = \frac{1}{2} \times 0.1 \times (2^2) = \frac{1}{2} \times 0.1 \times 4 = 0.2 \, \text{J} \][/tex]
3. Calculating Total Mechanical Energy (TME)
- The total mechanical energy is the sum of potential and kinetic energies:
[tex]\[ TME = PE + KE \][/tex]
Substituting the computed values of potential and kinetic energy:
[tex]\[ TME = 1.47 \, \text{J} + 0.2 \, \text{J} = 1.67 \, \text{J} \][/tex]
Thus, the total mechanical energy of the paper airplane is [tex]\( \boxed{1.67 \, \text{J}} \)[/tex]. So, the correct answer is:
[tex]\[ \boxed{B. \, 1.67 J} \][/tex]
