Two skiers, Annie and Jack, start skiing from rest at different points on a hill

Question

Two skiers, Annie and Jack, start skiing from rest at different points on a hill at the same time. Jack, with mass 94 kg, skis from the top of the hill down a steeper section with an angle of inclination of 35°. Annie, with mass 65 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 150 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.)

Explanation / Answer

150m *sin(35) = 86m vertical drop 150 cos(35) =122.9 m advance horizontal = position the vertical component of mass is 86/150 *94kg and the vertical acceleration will be 86/150*9.81 m/sec^2 = 5.62m/sec^2 v =1/2At^2 86 = 1/2 *5.62*t^2 t=5.53s V upon arrival at less steep section = 5.53*5.62 =31.1 m/s

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