Question

A 70.0-kg skier rides a 2780-m-long lift to the top of a mountain. The lift makes an angle of 14.7° with the horizontal. What is the change in the skier's gravitational potential energy? A 70.0-kg skier rides a 2780-m-long lift to the top of a mountain. The lift makes an angle of 14.7° with the horizontal. What is the change in the skier's gravitational potential energy? @Physics

Answer 1

\[\Large PE = mgh\]Assuming g and m remain constant, h is the only changing factor - the skier's height above Earth. If the lift is 2780m at 14.7° above the horizontal, then the vertical distance will be 2780 * sin(14.7) = 705m (3 s.f.).

So her potential energy will be:
\[\Large \begin{array}{l}
PE = 70 \cdot 9.81 \cdot 705\\
= {\rm{484,123}}{\rm{.5}}\\
= 4.84 \times {10^3}J
\end{array}\]
If you're doing either high-school or introductory physics, this is probably all you're being asked. If it's a slightly higher level, you may be expected to work it out based on the gravitational potential energy equation:
\[\Large U = - G\frac{{Mm}}{r}\]
But given the question I'd assume not =)