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Answer :
To find the mass of the skier given their potential energy and height, we can use the formula for gravitational potential energy:
[tex]\[ \text{Potential Energy (PE)} = m \times g \times h \][/tex]
where:
- [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],
- [tex]\( h \)[/tex] is the height in meters.
We need to rearrange this formula to solve for mass ([tex]\( m \)[/tex]):
[tex]\[ m = \frac{\text{PE}}{g \times h} \][/tex]
Given:
- Potential Energy ([tex]\( \text{PE} \)[/tex]) = 137,200 J
- Height ([tex]\( h \)[/tex]) = 200 m
- Acceleration due to gravity ([tex]\( g \)[/tex]) = 9.81 m/s²
Substitute these values into the rearranged formula:
[tex]\[ m = \frac{137,200}{9.81 \times 200} \][/tex]
When you carry out the division:
[tex]\[ m = \frac{137,200}{1,962} \][/tex]
[tex]\[ m \approx 69.93 \, \text{kg} \][/tex]
So, the mass of the skier is approximately 70 kg.
[tex]\[ \text{Potential Energy (PE)} = m \times g \times h \][/tex]
where:
- [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],
- [tex]\( h \)[/tex] is the height in meters.
We need to rearrange this formula to solve for mass ([tex]\( m \)[/tex]):
[tex]\[ m = \frac{\text{PE}}{g \times h} \][/tex]
Given:
- Potential Energy ([tex]\( \text{PE} \)[/tex]) = 137,200 J
- Height ([tex]\( h \)[/tex]) = 200 m
- Acceleration due to gravity ([tex]\( g \)[/tex]) = 9.81 m/s²
Substitute these values into the rearranged formula:
[tex]\[ m = \frac{137,200}{9.81 \times 200} \][/tex]
When you carry out the division:
[tex]\[ m = \frac{137,200}{1,962} \][/tex]
[tex]\[ m \approx 69.93 \, \text{kg} \][/tex]
So, the mass of the skier is approximately 70 kg.
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