The elevation at the base of a skill is 350 m above sea level. A ski lift raises a skier (total mass = 72 kg, including equipment) to the top of the hill. If the skier's gravitational potential energy relative to the base of the hill is now 9.2 x 10^5 J, what is the elevation at the top of the hill?

Question

anonymous · Answer

*hill

anonymous · Answer

Okay, so you know that the potential energy (U) of the skier at the top of the hill is $$U= 9.2\times10^{5} J = mgh$$ where g is the gravitational acceraltion of the Earth, m is the mass of the skier plus equipment and h is the height (or distance that ski lift raised the skier to). In this case 

                                  h = the height of the hill relative to its base
Therefore the elevation (H) of the top of the hill relative to sea level is $$H=U/mg+350m$$

anonymous · Answer

so I add 350 not subtract?

anonymous · Answer

and why do I add 350 m?

anonymous · Answer

Yes, if the base of the hll is 350 m above sea level then the top of the hill is more than that above sea level. Why do you feel you should subtract?

anonymous · Answer

to get the elevation at the top pf the hill?

anonymous · Answer

The ski lift raised the skier from the base of the hill to the top of the hill. So the the value for the height (h) is also relative from the base of the hill and not relative from sea level. This is because the skier was at the base of the hill to start with. If he had been at sea level and the ski lift raised him from there to the top of the hill then you would need to subtract 350 m.

anonymous · Answer

ohh.. thank you!

anonymous · Answer

My pleasure

anonymous · Answer

Correction to the comment  "If he had been at sea level and the ski lift raised him from there to the top of the hill then you would need to subtract 350 m. " This statement is in correct. If the ski lift had raised the skier from sea level to the top of the hill then $$H =U/mg$$ That is, you wouldn't need to add, or for that matter, subtract anything. Sorry for misleading you. Just to be clear, the word "elevation" in this context means the distance relative to sea level.

anonymous · Answer

Let  the height of the hill be "x" metres. Use the potential energy formula and equate wiht the total energy given. Here,  required height = (350 + x)metres, "g" = 10 m/s^2(for easy calculation), and given mass = 72 kg.

So, according to formula, we have,
(350 + x) * 10 * 72 = 9.2 * 10^5

Equate and solve.