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Answer :
To find the mass of the skier, we need to use the formula for gravitational potential energy:
[tex]\[ \text{Potential Energy (PE)} = m \times g \times h \][/tex]
where:
- [tex]\( \text{PE} \)[/tex] is the potential energy in joules,
- [tex]\( m \)[/tex] is the mass 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.
We have been provided with:
- Potential energy ([tex]\( \text{PE} \)[/tex]) = 137,200 J,
- Height ([tex]\( h \)[/tex]) = 200 m.
We need to rearrange the formula to solve for mass ([tex]\( m \)[/tex]):
[tex]\[ m = \frac{\text{PE}}{g \times h} \][/tex]
Substitute the given values into the formula:
[tex]\[ m = \frac{137,200 \, \text{J}}{9.81 \, \text{m/s}^2 \times 200 \, \text{m}} \][/tex]
After performing the calculations, the mass ([tex]\( m \)[/tex]) of the skier is found to be approximately 70 kg.
Among the given options, 70 kg is the correct answer.
[tex]\[ \text{Potential Energy (PE)} = m \times g \times h \][/tex]
where:
- [tex]\( \text{PE} \)[/tex] is the potential energy in joules,
- [tex]\( m \)[/tex] is the mass 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.
We have been provided with:
- Potential energy ([tex]\( \text{PE} \)[/tex]) = 137,200 J,
- Height ([tex]\( h \)[/tex]) = 200 m.
We need to rearrange the formula to solve for mass ([tex]\( m \)[/tex]):
[tex]\[ m = \frac{\text{PE}}{g \times h} \][/tex]
Substitute the given values into the formula:
[tex]\[ m = \frac{137,200 \, \text{J}}{9.81 \, \text{m/s}^2 \times 200 \, \text{m}} \][/tex]
After performing the calculations, the mass ([tex]\( m \)[/tex]) of the skier is found to be approximately 70 kg.
Among the given options, 70 kg is the correct answer.
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