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(55pt) Consider the motion of a skier of mass am. down a track with a constant slope 19. The friction of the skies is negligible, but the motion is subject to air resistance. The resistance force is given by f : kv2. The initial velocity of the skier is equal to zero. Figure 1: A skier. (a) (lOpt) What is the velocity of the skier as a function of time? (b) (let) What is the distance l traveled by the skier as a function of time? (c) (lUpt) How far does he travel by the time his velocity reaches approximately 90% of its maximum possible value? ((1) (5pt) The coefcient of air resistance is approximately given by k = pA/2, where p is the density of air and A is the crosssectional area of the skier. Taking p = 1 kg m'3? A = 1 m2, m = 100 kg and 6 = 45 ,estimate the length I needed to achieve 90% of the maximum velocity. How does it compare with the length of a typical ski jump track of about 100 In