High School

A skier with a potential energy of [tex]$137,200 J$[/tex] waits on top of a ski jump that is 200 m high. What is the mass of the skier?

A. 20 kg
B. 70 kg
C. 137 kg
D. 686 kg

Answer :

To find the mass of the skier, we use the formula for potential energy:

[tex]\[ \text{Potential Energy (PE)} = m \times g \times h \][/tex]

where:
- [tex]\( \text{PE} \)[/tex] is the potential energy, which is given as [tex]\( 137,200 \, \text{Joules} \)[/tex].
- [tex]\( m \)[/tex] is the mass of the skier, which we need to find.
- [tex]\( g \)[/tex] is the acceleration due to gravity, approximately [tex]\( 9.8 \, \text{m/s}^2 \)[/tex].
- [tex]\( h \)[/tex] is the height of the ski jump, which is [tex]\( 200 \, \text{meters} \)[/tex].

To solve for the mass [tex]\( m \)[/tex], we rearrange the formula:

[tex]\[ m = \frac{\text{PE}}{g \times h} \][/tex]

By plugging in the known values:

[tex]\[ m = \frac{137,200}{9.8 \times 200} \][/tex]

[tex]\[ m = \frac{137,200}{1,960} \][/tex]

When you divide [tex]\( 137,200 \)[/tex] by [tex]\( 1,960 \)[/tex], you get approximately [tex]\( 70 \)[/tex].

So, the mass of the skier is approximately [tex]\( 70 \, \text{kg} \)[/tex]. The closest option from the choices provided is [tex]\( 70 \, \text{kg} \)[/tex].