Answer :
We can use the formula for gravitational potential energy:
[tex]$$
PE = m \cdot g \cdot h
$$[/tex]
where
[tex]\( PE \)[/tex] is the potential energy,
[tex]\( m \)[/tex] is the mass,
[tex]\( g \)[/tex] is the acceleration due to gravity (approximately [tex]\(9.8 \, \text{m/s}^2\)[/tex]), and
[tex]\( h \)[/tex] is the height.
Given:
[tex]\[
PE = 137200 \, \text{J}, \quad h = 200 \, \text{m}, \quad g = 9.8 \, \text{m/s}^2
\][/tex]
We need to solve for [tex]\( m \)[/tex]. Rearranging the formula gives:
[tex]$$
m = \frac{PE}{g \cdot h}
$$[/tex]
Substitute the known values:
[tex]$$
m = \frac{137200}{9.8 \cdot 200}
$$[/tex]
Now, calculate the denominator:
[tex]$$
9.8 \cdot 200 = 1960
$$[/tex]
Thus:
[tex]$$
m = \frac{137200}{1960}
$$[/tex]
Dividing the values gives:
[tex]$$
m = 70 \, \text{kg}
$$[/tex]
Therefore, the mass of the skier is approximately [tex]\(\boxed{70 \, \text{kg}}\)[/tex].
[tex]$$
PE = m \cdot g \cdot h
$$[/tex]
where
[tex]\( PE \)[/tex] is the potential energy,
[tex]\( m \)[/tex] is the mass,
[tex]\( g \)[/tex] is the acceleration due to gravity (approximately [tex]\(9.8 \, \text{m/s}^2\)[/tex]), and
[tex]\( h \)[/tex] is the height.
Given:
[tex]\[
PE = 137200 \, \text{J}, \quad h = 200 \, \text{m}, \quad g = 9.8 \, \text{m/s}^2
\][/tex]
We need to solve for [tex]\( m \)[/tex]. Rearranging the formula gives:
[tex]$$
m = \frac{PE}{g \cdot h}
$$[/tex]
Substitute the known values:
[tex]$$
m = \frac{137200}{9.8 \cdot 200}
$$[/tex]
Now, calculate the denominator:
[tex]$$
9.8 \cdot 200 = 1960
$$[/tex]
Thus:
[tex]$$
m = \frac{137200}{1960}
$$[/tex]
Dividing the values gives:
[tex]$$
m = 70 \, \text{kg}
$$[/tex]
Therefore, the mass of the skier is approximately [tex]\(\boxed{70 \, \text{kg}}\)[/tex].
