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A snowboarder starts from rest on an inclined planar snow surface and gives herself a tiny push to start sliding down the hill. The coefficient of kinetic friction between her snowboard and the snow is 0.14. She notices that she travels 27.81 m horizontally and 39.78 m vertically (downward) before whizzing by a marker flag. How fast is she traveling as she passes the flag?

Respuesta :

Answer:

v = 26.52 m/s

Explanation:

Here we know that as she passes the flag she will gain some speed

so here we can say that

Work done by all forces = change in kinetic energy of the system

so we will have

[tex]W_g + W_f = \frac{1}{2}mv_f^2 - \frac{1}{2}mv_i^2[/tex]

here we know that

[tex]W_g = mgh[/tex]

[tex]W_f = -\mu mg d[/tex]

[tex]v_i = 0[/tex]

h = 39.78 m

d = 27.81 m

so we have

[tex]mgh - \mu mg d = \frac{1}{2}mv^2 - 0[/tex]

[tex](9.8)(39.78 - (0.14)(27.81)) = \frac{1}{2} v^2[/tex]

[tex]v = 26.52 m/s[/tex]

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