Referring to the “ Ski Jump Fail” video, assume the snow ramp height ( h ) is 2

Question

  Referring to the “Ski Jump Fail” video, assume the snow ramp height (h) is 2 m and the snow bank height (H) is 3.5 m, both measured from a horizontal datum at the start of the ramp. If the horizontal distance from the end of the ramp to the snow bank (s) is 10 m and the skier’s initial velocity (vo) leaving the ramp is 12 m/s, determine the minimum ramp angle that allows the skier to just clear the snow bank (neglecting air resistance). Sketch the trajectory of the skier for this angle on a scaled graph.

http://youtu.be/Cvg23EaRhUs

Explanation / Answer

For horizontal motion

Vcos theta x t = 10

t cos thet = 10/12

For vertical motion

3.5-2 = Vtsin theta - 0.5xg xt^2

1.5 = 10tantheta - 4.9x100sec^2 theta/144

1.5 = 10tan theta -3.4027 ( 1+ tan^2 theta )

4.9027 = 10tan theta -3.4027 tan^2 theta

solving

tan theta = 0.6218

theta = 31.87 degree

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