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Answer :
We start with the formula for gravitational potential energy:
[tex]$$
PE = mgh
$$[/tex]
where
[tex]\( PE \)[/tex] is the potential energy,
[tex]\( m \)[/tex] is the mass,
[tex]\( g \)[/tex] is the acceleration due to gravity (taken as [tex]\( 9.8 \, \text{m/s}^2 \)[/tex]), and
[tex]\( h \)[/tex] is the height.
Given the values:
- [tex]\( PE = 137200 \, \text{J} \)[/tex]
- [tex]\( h = 200 \, \text{m} \)[/tex]
- [tex]\( g = 9.8 \, \text{m/s}^2 \)[/tex]
We rearrange the equation to solve for the mass [tex]\( m \)[/tex]:
[tex]$$
m = \frac{PE}{gh}
$$[/tex]
Next, we calculate the product [tex]\( gh \)[/tex]:
[tex]$$
gh = 9.8 \times 200 = 1960
$$[/tex]
Now, substitute the values into the formula for [tex]\( m \)[/tex]:
[tex]$$
m = \frac{137200}{1960} \approx 70 \, \text{kg}
$$[/tex]
Thus, the mass of the skier is [tex]\( 70 \, \text{kg} \)[/tex].
[tex]$$
PE = mgh
$$[/tex]
where
[tex]\( PE \)[/tex] is the potential energy,
[tex]\( m \)[/tex] is the mass,
[tex]\( g \)[/tex] is the acceleration due to gravity (taken as [tex]\( 9.8 \, \text{m/s}^2 \)[/tex]), and
[tex]\( h \)[/tex] is the height.
Given the values:
- [tex]\( PE = 137200 \, \text{J} \)[/tex]
- [tex]\( h = 200 \, \text{m} \)[/tex]
- [tex]\( g = 9.8 \, \text{m/s}^2 \)[/tex]
We rearrange the equation to solve for the mass [tex]\( m \)[/tex]:
[tex]$$
m = \frac{PE}{gh}
$$[/tex]
Next, we calculate the product [tex]\( gh \)[/tex]:
[tex]$$
gh = 9.8 \times 200 = 1960
$$[/tex]
Now, substitute the values into the formula for [tex]\( m \)[/tex]:
[tex]$$
m = \frac{137200}{1960} \approx 70 \, \text{kg}
$$[/tex]
Thus, the mass of the skier is [tex]\( 70 \, \text{kg} \)[/tex].
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