Answer :
To find the mass of the skier, we use the formula for potential energy:
[tex]\[ \text{Potential Energy} = \text{mass} \times \text{gravity} \times \text{height} \][/tex]
In this equation:
- Potential Energy (PE) is given as 137,200 Joules.
- Gravity (g) is approximately 9.8 m/s² (constant acceleration due to gravity).
- Height (h) is given as 200 meters.
We need to solve for the mass (m). To do this, rearrange the formula:
[tex]\[ \text{mass} = \frac{\text{Potential Energy}}{\text{gravity} \times \text{height}} \][/tex]
Substituting the given values:
[tex]\[ \text{mass} = \frac{137,200}{9.8 \times 200} \][/tex]
Calculate the denominator:
[tex]\[ 9.8 \times 200 = 1,960 \][/tex]
Then divide the potential energy by this result:
[tex]\[ \text{mass} = \frac{137,200}{1,960} \approx 70 \][/tex]
Therefore, the mass of the skier is approximately 70 kg. The closest option to this result is 70 kg.
[tex]\[ \text{Potential Energy} = \text{mass} \times \text{gravity} \times \text{height} \][/tex]
In this equation:
- Potential Energy (PE) is given as 137,200 Joules.
- Gravity (g) is approximately 9.8 m/s² (constant acceleration due to gravity).
- Height (h) is given as 200 meters.
We need to solve for the mass (m). To do this, rearrange the formula:
[tex]\[ \text{mass} = \frac{\text{Potential Energy}}{\text{gravity} \times \text{height}} \][/tex]
Substituting the given values:
[tex]\[ \text{mass} = \frac{137,200}{9.8 \times 200} \][/tex]
Calculate the denominator:
[tex]\[ 9.8 \times 200 = 1,960 \][/tex]
Then divide the potential energy by this result:
[tex]\[ \text{mass} = \frac{137,200}{1,960} \approx 70 \][/tex]
Therefore, the mass of the skier is approximately 70 kg. The closest option to this result is 70 kg.
