# Work problem

by rsala
Tags: work
 P: 40 1. The problem statement, all variables and given/known data A skier moving at 5.00 m/s encounters a long, rough horizontal patch of snow having coefficient of kinetic friction 0.220 with her skis. the patch is 2.9 meters long. what is her velocity after passing the patch? problem must be solved by using work, avoid newtons 2. Relevant equations work = fs work = $$K_{final} - K_{initial} =- \frac{1}{2}m v^{2}_{final}- \frac{1}{2}m v^{2}_{initial}$$ 3. The attempt at a solution let s be displacement (2.9m) $$-\mu_{k}mg*s = - \frac{1}{2}m v^{2}_{final}- \frac{1}{2} m v^{2}_{initial}$$ m is irrelevant, factor it out and cancel. $$-\mu_{k}g*s = - \frac{1}{2} v^{2}_{final}- \frac{1}{2} v^{2}_{initial}$$ solve for $$v_{final}$$ $$\frac{-\mu_{k}gs+.5v^{2}_{initial}}{-.5} = v^{2}_{final}$$ $$\sqrt{-2(-\mu_{k}gs+\frac{1}{2}v^{2}_{initial})} = v_{final}$$ $$\sqrt{ -12.4952}$$ cannot take sqrt of negative number. i can't go beyond this part, is there a solution?
 Sci Advisor HW Helper Thanks P: 25,235 $$\mu_{k}g*s = \frac{1}{2} v^{2}_{initial}- \frac{1}{2} v^{2}_{final}$$ Where are you finding all the extra minus signs?
 P: 40 in which part