Math  /  Algebra

Question24. (II) A 68kg68-\mathrm{kg} snowboarder has an initial velocity of 5.0 m/s5.0 \mathrm{~m} / \mathrm{s} at the top of a 2828^{\circ} incline (Fig. 5-37). After sliding down the 110m110-\mathrm{m}-long incline (assume a coefficient of kinetic friction μk=0.18\mu_{\mathrm{k}}=0.18 ), the snowboarder has attained a velocity vv. The snowboarder then slides along a flat surface (on which μk=0.15)\left.\mu_{\mathrm{k}}=0.15\right) and comes to rest after a distance xx. 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 xx. Ignore air resistance.

Studdy Solution
Determine the distance x x on the flat surface where the snowboarder comes to rest.
Use the kinematic equation:
v2=u2+2aflatx v^2 = u^2 + 2a_{\text{flat}} x
where v=0 v = 0 (final velocity), u u is the velocity at the bottom of the incline calculated in STEP_2, and aflat a_{\text{flat}} is the acceleration on the flat surface calculated in STEP_3.
Solve for x x :
0=u2+2aflatx 0 = u^2 + 2a_{\text{flat}} x x=u22aflat x = -\frac{u^2}{2a_{\text{flat}}}
Calculate x x .

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