Answer :
To find the mass of the skier with a potential energy of 137,200 Joules at the top of a 200 meter high ski jump, we can use the formula for potential energy:
[tex]\[
PE = m \cdot g \cdot h
\][/tex]
where:
- [tex]\( PE \)[/tex] is the potential energy,
- [tex]\( m \)[/tex] is the mass of the object,
- [tex]\( g \)[/tex] is the acceleration due to gravity (approximately [tex]\( 9.81 \, \text{m/s}^2 \)[/tex] on Earth),
- [tex]\( h \)[/tex] is the height above the reference point.
We need to solve for the mass [tex]\( m \)[/tex]. Rearranging the equation gives us:
[tex]\[
m = \frac{PE}{g \cdot h}
\][/tex]
Now, plug in the given values:
- [tex]\( PE = 137,200 \, \text{J} \)[/tex]
- [tex]\( g = 9.81 \, \text{m/s}^2 \)[/tex]
- [tex]\( h = 200 \, \text{m} \)[/tex]
Substituting these values into the equation:
[tex]\[
m = \frac{137,200}{9.81 \times 200}
\][/tex]
Upon calculating, we find:
[tex]\[
m \approx 69.93 \, \text{kg}
\][/tex]
Since we need to choose the closest mass from the given options, the skier's mass is approximately 70 kg.
[tex]\[
PE = m \cdot g \cdot h
\][/tex]
where:
- [tex]\( PE \)[/tex] is the potential energy,
- [tex]\( m \)[/tex] is the mass of the object,
- [tex]\( g \)[/tex] is the acceleration due to gravity (approximately [tex]\( 9.81 \, \text{m/s}^2 \)[/tex] on Earth),
- [tex]\( h \)[/tex] is the height above the reference point.
We need to solve for the mass [tex]\( m \)[/tex]. Rearranging the equation gives us:
[tex]\[
m = \frac{PE}{g \cdot h}
\][/tex]
Now, plug in the given values:
- [tex]\( PE = 137,200 \, \text{J} \)[/tex]
- [tex]\( g = 9.81 \, \text{m/s}^2 \)[/tex]
- [tex]\( h = 200 \, \text{m} \)[/tex]
Substituting these values into the equation:
[tex]\[
m = \frac{137,200}{9.81 \times 200}
\][/tex]
Upon calculating, we find:
[tex]\[
m \approx 69.93 \, \text{kg}
\][/tex]
Since we need to choose the closest mass from the given options, the skier's mass is approximately 70 kg.
