Question

In a downhill ski race surprisingly little advantage is gained by getting a running start. (This is because the initial kinetic energy is small compared with the gain in gravitational potential energy even in small hills) to demonstrate this , find the final speed in m/s and the time taken in seconds for a skier who skies 68.0 m along a 27degree slope neglecting friction for the following cases (enter the final speeds to at least one decimal place . A. Starting from rest

Final speed ________. m/s. Time taken ______s

B starting with an initial speed of 3.50 m/s

Final speed ______m/s

Time taken _______s

Answer 1

To demonstrate this, find the final speed and the time taken for a skier who skies S = 68.0 m along a theta = 27° slope neglecting friction for the following two cases.

NOTE: That the fall line is h = S sin(theta) = 68sin27= 30.87 m.

(a) starting from rest U = 0

So V = sqrt(2gh) = sqrt(2*9.8*30.870) = 24.6 m/s.

And from T = S/Vavg = 68/(24.2/2) = 5.53 seconds.


(b) starting with an initial speed of U = 3.50 m/s

So V = sqrt(U^2 + 2gh) = sqrt(12.25 + 24.6^2) = 27.48 m/s.

And T = 68/((3.5+ 27.48)/2) = 4.38 seconds.

Hope this helps.

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