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Answer :
We start with the formula for gravitational potential energy:
[tex]$$
U = mgh,
$$[/tex]
where
[tex]\( U \)[/tex] is the potential energy,
[tex]\( m \)[/tex] is the mass,
[tex]\( g \)[/tex] is the gravitational acceleration, and
[tex]\( h \)[/tex] is the height.
Given that the potential energy [tex]\( U \)[/tex] is [tex]\( 137200 \, J \)[/tex] and the height [tex]\( h \)[/tex] is [tex]\( 200 \, m \)[/tex], and using [tex]\( g = 9.8 \, m/s^2 \)[/tex], we solve for the mass [tex]\( m \)[/tex] by rearranging the equation:
[tex]$$
m = \frac{U}{gh}.
$$[/tex]
Substitute the known values:
[tex]$$
m = \frac{137200}{9.8 \times 200}.
$$[/tex]
First, calculate the product in the denominator:
[tex]$$
9.8 \times 200 = 1960.
$$[/tex]
Now, divide to find the mass:
[tex]$$
m = \frac{137200}{1960} = 70 \, \text{kg}.
$$[/tex]
Thus, the mass of the skier is [tex]\( 70 \, \text{kg} \)[/tex].
[tex]$$
U = mgh,
$$[/tex]
where
[tex]\( U \)[/tex] is the potential energy,
[tex]\( m \)[/tex] is the mass,
[tex]\( g \)[/tex] is the gravitational acceleration, and
[tex]\( h \)[/tex] is the height.
Given that the potential energy [tex]\( U \)[/tex] is [tex]\( 137200 \, J \)[/tex] and the height [tex]\( h \)[/tex] is [tex]\( 200 \, m \)[/tex], and using [tex]\( g = 9.8 \, m/s^2 \)[/tex], we solve for the mass [tex]\( m \)[/tex] by rearranging the equation:
[tex]$$
m = \frac{U}{gh}.
$$[/tex]
Substitute the known values:
[tex]$$
m = \frac{137200}{9.8 \times 200}.
$$[/tex]
First, calculate the product in the denominator:
[tex]$$
9.8 \times 200 = 1960.
$$[/tex]
Now, divide to find the mass:
[tex]$$
m = \frac{137200}{1960} = 70 \, \text{kg}.
$$[/tex]
Thus, the mass of the skier is [tex]\( 70 \, \text{kg} \)[/tex].
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