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Answer :
To determine the mass of the skier, we need to use the formula for gravitational potential energy:
[tex]\[ \text{Potential Energy (PE)} = \text{mass (m)} \times \text{gravity (g)} \times \text{height (h)} \][/tex]
Where:
- Potential energy (PE) is given as [tex]\(137,200 \, \text{Joules (J)}\)[/tex].
- Gravity (g) is approximately [tex]\(9.81 \, \text{meters per second squared (m/s}^2)\)[/tex].
- Height (h) is given as [tex]\(200 \, \text{meters (m)}\)[/tex].
To find the mass (m), we rearrange the formula:
[tex]\[ \text{mass (m)} = \frac{\text{Potential Energy (PE)}}{\text{gravity (g)} \times \text{height (h)}} \][/tex]
Substituting the given values:
[tex]\[ \text{mass (m)} = \frac{137,200}{9.81 \times 200} \][/tex]
[tex]\[ \text{mass (m)} \approx \frac{137,200}{1,962} \][/tex]
[tex]\[ \text{mass (m)} \approx 69.93 \, \text{kg} \][/tex]
Rounding this to the nearest whole number, the mass of the skier is approximately [tex]\(70 \, \text{kg}\)[/tex].
Therefore, the correct answer is [tex]\(70 \, \text{kg}\)[/tex].
[tex]\[ \text{Potential Energy (PE)} = \text{mass (m)} \times \text{gravity (g)} \times \text{height (h)} \][/tex]
Where:
- Potential energy (PE) is given as [tex]\(137,200 \, \text{Joules (J)}\)[/tex].
- Gravity (g) is approximately [tex]\(9.81 \, \text{meters per second squared (m/s}^2)\)[/tex].
- Height (h) is given as [tex]\(200 \, \text{meters (m)}\)[/tex].
To find the mass (m), we rearrange the formula:
[tex]\[ \text{mass (m)} = \frac{\text{Potential Energy (PE)}}{\text{gravity (g)} \times \text{height (h)}} \][/tex]
Substituting the given values:
[tex]\[ \text{mass (m)} = \frac{137,200}{9.81 \times 200} \][/tex]
[tex]\[ \text{mass (m)} \approx \frac{137,200}{1,962} \][/tex]
[tex]\[ \text{mass (m)} \approx 69.93 \, \text{kg} \][/tex]
Rounding this to the nearest whole number, the mass of the skier is approximately [tex]\(70 \, \text{kg}\)[/tex].
Therefore, the correct answer is [tex]\(70 \, \text{kg}\)[/tex].
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