A 75-kg snowboarder has an initial velocity of 5.0 m/s at the top of a 28degree

Question

A 75-kg snowboarder has an initial velocity of 5.0 m/s at the top of a 28degree incline (Fig. 4-75). After sliding down the 110-m-long incline (on which the coefficient of kinetic friction is muk = 0.18), the snowboarder has attained a velocity v. The snowboarder then slides along a flat surface (on which muk = 0.15) and comes to rest after a distance x. Use Newton's second law to find the snowboarder's acceleration while on the incline and while on the flat surface. Then use these accelerations to determine x.

Explanation / Answer

acc. on incline :

mgsin28 - 0.18mgcos28 = ma

a = gsin28 - 0.18cos28 = 2.92 m/s2

acc. on flat surface :

a = - f/m = 0.15 x m x g /m = 0.18g = 1.76 m/s2

for incline :

v^2 - u^2 = 2ad

v^2 - 5^2 = 2 x 2.92 x 110

v = 25.83 m/s

for flat surface :

v^2 - u^2 = 2ad

0 - 25.83^3 = 2 x -1.76 x d

d = 189.60 m

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