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 a mass 98.9 kg, skis from the top of the hill down a steeper section with an angle of inclination of 35.0 degree. Annie, with mass 59.3 kg, starts from a lower point and skis a less steep section, with an angle of inclination of 20.0 degree. The length of the steeper section is 100 m. Determine the acceleration of the combined center of mass for Annie and Jack before Jack reaches the less steep section. ax = ; ay = Tries 0/99

Explanation / Answer

acc. of jack ,

aj = gsin35 m/s2 below 35 degree

aj = gsin35 ( cos35i - sin35 j )

= 4.60 i - 3.22 j m/s2
  
  
  
  
aA = gsin20 below 20 degree

= gsin20 ( cos20 i - sin20 j)
  
= 3.15 i - 1.15 j m/s2



ax = 98.9 x 4.60 + 59.3 x 3.15 / (98.9 + 59.3)

= 4.06 m/s2




ay = - 98.9 x 3.22 - 59.3x 1.15 / (98.9 + 59.3)

= - 2.44 m/s2

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