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# Answer to Question #102185 in Mechanics | Relativity for dfdd

Question #102185
A 62.7 kg skier rides a 916.6 m long lift to the top of a mountain. The lift makes an angle of 28.3o with the horizontal. How fast will she be traveling when she reaches the bottom of the mountain?
1
2020-02-10T09:23:40-0500

If we neglect friction, all we have to do is to use the conservation of energy: potential energy converts to kinetic energy. At the highest point the potential energy is

"PE=mgH=mg\\cdot L\\text{ sin}\\theta."

At the bottom this energy will turn into kinetic energy:

"KE=\\frac{1}{2}mv^2."

Since

"PE=KE,\\\\\n\\space\\\\\nmg\\cdot L\\text{ sin}\\theta=\\frac{1}{2}mv^2,\\\\\n\\space\\\\\nv=\\sqrt{2gL\\text{ sin}\\theta}=\\\\=\\sqrt{2\\cdot9.81\\cdot916.6\\cdot\\text{sin}28.3^\\circ}=92.3\\text{ m\/s}."

As we see, the final velocity does not depend on the mass the skier.

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