Answer :
To find the mass of the skier, we can use the formula for gravitational potential energy:
[tex]\[ \text{Potential Energy (PE)} = m \times g \times h \][/tex]
where:
- [tex]\( PE \)[/tex] is the potential energy, which is 137,200 Joules.
- [tex]\( m \)[/tex] is the mass of the skier, which we need to find.
- [tex]\( g \)[/tex] is the acceleration due to gravity, approximately 9.8 m/s².
- [tex]\( h \)[/tex] is the height, which is 200 meters.
We're given all the values except for the mass, so we'll rearrange the formula to solve for [tex]\( m \)[/tex]:
[tex]\[ m = \frac{PE}{g \times h} \][/tex]
Now, substitute the given values into the formula:
[tex]\[ m = \frac{137,200}{9.8 \times 200} \][/tex]
Simplify the calculation:
[tex]\[ m = \frac{137,200}{1,960} \][/tex]
[tex]\[ m \approx 70 \][/tex]
The mass of the skier is approximately 70 kg. Therefore, the correct answer is 70 kg.
[tex]\[ \text{Potential Energy (PE)} = m \times g \times h \][/tex]
where:
- [tex]\( PE \)[/tex] is the potential energy, which is 137,200 Joules.
- [tex]\( m \)[/tex] is the mass of the skier, which we need to find.
- [tex]\( g \)[/tex] is the acceleration due to gravity, approximately 9.8 m/s².
- [tex]\( h \)[/tex] is the height, which is 200 meters.
We're given all the values except for the mass, so we'll rearrange the formula to solve for [tex]\( m \)[/tex]:
[tex]\[ m = \frac{PE}{g \times h} \][/tex]
Now, substitute the given values into the formula:
[tex]\[ m = \frac{137,200}{9.8 \times 200} \][/tex]
Simplify the calculation:
[tex]\[ m = \frac{137,200}{1,960} \][/tex]
[tex]\[ m \approx 70 \][/tex]
The mass of the skier is approximately 70 kg. Therefore, the correct answer is 70 kg.
