There are two questions in this picture. Two snowy peaks are 706 m and 666 m abo

Question

There are two questions in this picture. Two snowy peaks are 706 m and 666 m above the valley between them. A ski run extends down from the top of the higher peak and then back up to the top of the lower one, with a total length of 3.5 km and an average slope of 26.0. A slider starts from rest on the higher peak. At what speed will she arrive at the top of the lower peak if the coasts without the poles? Ignore friction. Approximately what coefficient of kinetic friction between the snow and skis would make the skier stop just at that top of the lower peak?

Explanation / Answer

Initial Kinetic Energy = 0
Initial Potential Energy = m*g*h1
Final Kinetic Energy = 1/2 * mv^2
Final Potential Energy = m*g*h2

Using Energy Conservation
K.Ein + P.Ein = K.Efin + P.Efin
0 + m*g*h1 = 1/2 * mv^2 + m*g*h2
g*(h1 - h2) = 1/2 * v^2
9.8*(766 - 666) = 1/2 * v^2
v = 44.3 m/s
Speed at which she will arrive, v = 44.3 m/s

For Friction to stop at the other peak,
Work done against Friction = 1/2 * mv^2
Fs*d = 1/2 * m * 44.3^2
us*m*g*cos(26.0) * 3.5 * 10^3 = 1/2 * m*44.3^2
us*9.8*cos(26.0) * 3.5 * 10^3 = 1/2 *44.3^2
us = 0.044
Coefficient of kinetic friction needed, us = 0.044

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