Two skiers, Annie and Jack, start skiing from rest at different points on a hill
ID: 1965561 • Letter: T
Question
Two skiers, Annie and Jack, start skiing from rest at different points on a hill at the same time. Jack, with mass 85 kg, skis from the top of the hill down a steeper section with an angle of inclination of 35°. Annie, with mass 66 kg, starts from a lower point and skis a less steep section, with an angle of inclination of 20°. The length of the steeper section is 115 m. Determine the acceleration, velocity, and position vectors of the combined center of mass for Annie and Jack as a function of time before Jack reaches the less steep section. (Use the following variable as necessary: t, where t is the time before Jack reaches the less steep section.)
= _________________ + __________________ m/s2 = _________________ + __________________ m/s = __________________ + _________________ m from where Jack startedExplanation / Answer
the direction in which jack is travelling is : ( cos35 i - sin35 j) = .819i - .5725j acceleration of jack (a1) is only in the direction of the slope = m1*g*sin35 = 478.2767 m/s^2. the direction in which annie is travelling is : ( cos20 i - sin20 j) = .9397i - 0.342j acceleration of annie (a2) is only in the direction of the slope = m2 *g*sin20 =221.444 m/s^2. distance travelled along the slope = 115 m= .5*a1*t^2 => t = 0.69346 s. acceleration of center of mass (a) = (m1a1 +m2a2)/(m1+m2) = .563*478.2767(.819i - .5725j) + .437*221.444* (.9397i - 0.342j) = 311.4676i - 187.2526j m/s2. velocity of the center of mass = acceleration * time = a*t = 215.99i - 129.8522j m/s. position vector of center of mass = .5*a*t^2 in the direction of acceleration = 74.89i - 45.0236j m from the initial position
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