You are designing a \"Big Air\" ski jump ramp for the next Winter Olympics. You

Question

You are designing a "Big Air" ski jump ramp for the next Winter Olympics. You need to calculate the vertical height h from the starting point at the top of the ramp to the bottom of the ramp. The skiers push off hard with their skis as they start so they typically have a speed of 2.0 m/s at the top of the ramp. For safety, the skiers should have a speed of no more than 30.0 m/s when they reach the bottom of the ramp. You determine that for a 90.0 kg skier with good form, friction and air resistance will do total work of magnitude 4000 J on him during his run down the slope.

A.  What is the height h for which the skiers will reach the maximum safe speed?  

Explanation / Answer

V1 = speed of 2.0 m/s

V2 = 30.0 m/s

m = 90.0 kg

W = total work of magnitude 4000 J

KE1 + U1 = KE2 + U2 + W

0.5 m V12 + m g h = 0.5 m V22 + U2 + W

0.5 X 90 X 22 + 90 X 9.8 X h = 0.5 X 90 X 302 + 0 + 4000

180 + 882 h = 40500 + 4000

882 h = 44500 - 180

h = 50.249 m

the height h for which the skiers will reach the maximum safe speed is h = 50.249 m

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