Ski Jump Ramp. You are designing a ski jump ramp for the next Winter Olympics. You need to calculate the vertical height ?h? from the starting gate to the bottom of the ramp. The skiers push off hard with their ski poles at the start, just above the starting gate, so they typically have a speed of 2.0 m/s as they reach the gate. For safety, the skiers should have a speed no higher than 30.0 m/s when they reach the bottom of the ramp. You determine that for a 85.0-kg skier with good form, friction and air resistance will do total work of magnitude 4000 J on him during his run down the ramp. What is the maximum height ?h? for which the maximum safe speed will not be exceeded?

Solution 52P Step 1 of 5: Skier with mass m=85 kg pushes with the initial velocity v =2 m/s and reaches the i bottom with the speed v =30 m/s with height h from top to bottom under the influence of f work done by friction and air resistance of W=4000 J. As shown in the figure below Step 2 of 5: Given data, Mass, m=85 kg Initial speed, v =2 m/s i Final speed, v =30 m/s f External work done, W= 4000 J To find, Height , h= Step 3 of 5: In the given case the total mechanical energy is not conserved: Hence When forces other than the gravitational and elastic forces do work on a particle, the work done by these other forces equals the change in total mechanical energy (kinetic energy plus total potential energy). That is, K +iP + i = K + P f f Where K is kinetic energy and P is potential energy. Using K = mv and P= mgh 2 1 mv + 0 + W = mv + mgh 2 2 i 2 f