4. (From an old exam) In the 2006 Winter Olympics, Thomas Morgenstern of Austria won a gold medal in one of the ski jumping events; his longest jump was R = 140.0 m. The picture below shows a simplified diagram of his jump. (It's not to scale.) 150 140 m He takes off from point A at an angle of a = 15.0° above the horizontal, with an initial speed v0 = 26.9 m/s. The dotted curve roughly shows his trajectory; he lands at point B. Notice that the landing hill is curved, and is quite steep near point B. You should ignore air resistance in this problem. a) How long is he in the air? (That is, how long does it take him to get from A to B?) b) Find the magnitude and direction of his velocity just before he lands at B. c) Based on your answer to part (b), explain why it is safer for ski jumpers to land on a steep slope than on a flat surface. (Hint: a large sudden change in velocity requires a large impact force.)

4. (From an old exam) In the 2006 Winter Olympics, Thomas Morgenstern of Austria won a gold medal in one of the ski jumping events; his longest jump was R = 140.0 m. The picture below shows a simplified diagram of his jump. (It's not to scale.) 150 140 m He takes off from point A at an angle of a = 15.0° above the horizontal, with an initial speed v0 = 26.9 m/s. The dotted curve roughly shows his trajectory; he lands at point B. Notice that the landing hill is curved, and is quite steep near point B. You should ignore air resistance in this problem. a) How long is he in the air? (That is, how long does it take him to get from A to B?) b) Find the magnitude and direction of his velocity just before he lands at B. c) Based on your answer to part (b), explain why it is safer for ski jumpers to land on a steep slope than on a flat surface. (Hint: a large sudden change in velocity requires a large impact force.)