How far will he coast along the level area at the bottom of the slope?

116 m-during the entire descent down the hill, gravity is doing work on the skier and friction is doing negative work on the skier. friction is a non-conservative force and will alter the total mechanical energy of the skier. the equation to be used is kei + pei + wnc = kef + pef if we designate the level area at the bottom of the slope as the zero level of potential energy, then pef is 0 j. since the skier eventually stops (due to the effect of friction along the level area), the kef is 0 j. so the above equation becomes kei + pei + wnc = 0 the wnc term has two parts; there is friction doing along the inclined plane and friction doing work along the level surface. since these two sections of the motion have different normal forces and friction coefficients (and therefore friction forces), they will have to be treated separately. the graphic below depicts the free-body diagrams and the means by which the friction force can be determined. by substituting values of mu and mass and g and theta into the above equations, one finds that the friction values are on incline ffrict = 72.3 n on level surface ffrict = 384 n these forces act upon the skier over different distances. in the case of the inclined plane, the distance (d) can be computed from the given incline angle and the initial height. the relationship is depicted in the diagram below. the sine function is used to relate the angle to the initial height and the distance along the incline. in the case of the level surface, the distance is the unknown quantity (x) which this problem calls for.the distance d along the incline is d = hi / sin(theta) = 123 m / sin(14.1 deg) = 505 m now substitutions can be made into the work-energy equation and algebraic manipulation can be performed to solve for x: kei + pei + wnc = 0 kei + pei + wincline + wlevel = 0 0.5(62.9 kg)(12.9 m/s)2 + (62.9 kg)(9.8 m/s)(123 m) + (72.3 n)(505 m)cos(180 deg) + (384 n)(x)cos(180 deg) = 0 j 5233 j + 75820 j - 36512 j - 384 x = 0 j 44541 j = 384 x 116 m = x