Question

7. You should recall the homework problem about the ski jumper from Chapter 8. You might refer to that problem as you work through this slight variation on it. A skier of mass m starts from rest at a height H on a ski jump hill. She leaves the ramp at an angle 0, and achieves a peak height of h. Both heights, H and h, as shown in the diagram, are with respect to the launch point at the end of the ramp. Neglect the effects of air resistance and assume the ramp is frictionless. (a) [5] Apply the conservation of mechanical energy principle, (K+U)initial = (K +U)final to the Earth-skier system. Have the "initial" state be the skier at the top of the ski jump hill, and the "final" state be the skier at the launch point of the ramp. Use it to find a symbolic expression for the speed of the skier at the launch point. Then, use that result, and concepts from 2D projectile motion kinematics, to develop an expression for the velocity of the skier at the peak of her flight through the air, U peak- The only symbols that are allowed to appear in your symbolic expression for v peak are H, g, and 0. Put your symbolic vector answer in component form, v,and describe your reasoning as needed.v peak = (). (b) [5] Apply the conservation of mechanical energy principle again:(K+U)initial(K+U)inal: This time, have the "initial" state again be the skier at the top of the ski jump hill, but the "final" state be the skier at the peak of her flight through the air. Use this expression, in combination with your answer to part (a), to showt hat the height of the ski hill, H, is H=\frac{h}{\sin ^{2} \theta} For full credit, show all steps in the derivation and describe your reasoning as needed. (Note: You might need the Pythagorean identity, cos² 0 + sin? 0 = 1, to complete the derivation.)

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