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Answer :
To find the mass of the skier, we use the formula for potential energy:
[tex]\[ \text{Potential Energy (PE)} = m \times g \times h \][/tex]
where:
- [tex]\( \text{PE} \)[/tex] is the potential energy, which is given as [tex]\( 137,200 \, \text{Joules} \)[/tex].
- [tex]\( m \)[/tex] is the mass of the skier, which we need to find.
- [tex]\( g \)[/tex] is the acceleration due to gravity, approximately [tex]\( 9.8 \, \text{m/s}^2 \)[/tex].
- [tex]\( h \)[/tex] is the height of the ski jump, which is [tex]\( 200 \, \text{meters} \)[/tex].
To solve for the mass [tex]\( m \)[/tex], we rearrange the formula:
[tex]\[ m = \frac{\text{PE}}{g \times h} \][/tex]
By plugging in the known values:
[tex]\[ m = \frac{137,200}{9.8 \times 200} \][/tex]
[tex]\[ m = \frac{137,200}{1,960} \][/tex]
When you divide [tex]\( 137,200 \)[/tex] by [tex]\( 1,960 \)[/tex], you get approximately [tex]\( 70 \)[/tex].
So, the mass of the skier is approximately [tex]\( 70 \, \text{kg} \)[/tex]. The closest option from the choices provided is [tex]\( 70 \, \text{kg} \)[/tex].
[tex]\[ \text{Potential Energy (PE)} = m \times g \times h \][/tex]
where:
- [tex]\( \text{PE} \)[/tex] is the potential energy, which is given as [tex]\( 137,200 \, \text{Joules} \)[/tex].
- [tex]\( m \)[/tex] is the mass of the skier, which we need to find.
- [tex]\( g \)[/tex] is the acceleration due to gravity, approximately [tex]\( 9.8 \, \text{m/s}^2 \)[/tex].
- [tex]\( h \)[/tex] is the height of the ski jump, which is [tex]\( 200 \, \text{meters} \)[/tex].
To solve for the mass [tex]\( m \)[/tex], we rearrange the formula:
[tex]\[ m = \frac{\text{PE}}{g \times h} \][/tex]
By plugging in the known values:
[tex]\[ m = \frac{137,200}{9.8 \times 200} \][/tex]
[tex]\[ m = \frac{137,200}{1,960} \][/tex]
When you divide [tex]\( 137,200 \)[/tex] by [tex]\( 1,960 \)[/tex], you get approximately [tex]\( 70 \)[/tex].
So, the mass of the skier is approximately [tex]\( 70 \, \text{kg} \)[/tex]. The closest option from the choices provided is [tex]\( 70 \, \text{kg} \)[/tex].
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