And gun control is just one of many critical issues on which this nation appears to be at an impasse. Congress could not manage to restore even the most moderate restrictions on the sale of assault weapons to private citizens. It seems astonishing, but this spring, in the aftermath of a mass murder at an elementary school just twenty-five miles from here, the U.S. ![]() We are still suffering from the effects of the most severe recession since the Great Depression, and the American political system – once a global model of effective bipartisan governance – has become so polarized that it is nearly paralyzed. You, and I, are going to need time to figure out what’s next, time to consider where our true passions lie and how we might give them the fullest expression. As for the rest of you who are not so sure, I feel myself, for the first time in twenty years of Baccalaureate Addresses, in true communion. Congratulations! We wish you every success. Some of you know exactly what you want to do in the years ahead – whether it is medicine, the law, the military, starting a company, or – this year in particular – playing professional hockey. These pleasures now give way to a new set of challenges and opportunities as you explore the world that is all before you. In the course of all this activity, you have come to know yourselves more completely. You have lived four years in an environment of high energy and high achievement – in the classroom and the newsroom, on the stage and the athletic field, in the concert hall and the art studio, in community service and political debate. You have had access to extraordinary research laboratories, libraries, museums, and musical and dramatic performances. You know the words: “Lately it occurs to me, what a long, strange trip it’s been.” It’s been a long trip, but, for us, more wonderful than strange.Įach of you has had the opportunity to learn from teachers who are among the world’s most brilliant scholars, and to grow in the company of some of the most exceptional young adults to be found anywhere – your classmates. I find myself thinking about a Grateful Dead song written in 1970, the year I came to Yale as a graduate student. You leave Yale College after four years I leave the Yale Presidency after twenty. We used the results to estimate how much a moderate wind can modify a golf ball's range and suggested other possible applications.We leave together. Finally, we expressed in a parametric equation the locus of points corresponding to maximum heights for projectiles launched from the ground with the same initial speed in all directions. It turns out that a launch angle of 90° maximizes the time of flight, time of ascent, time of descent, and maximum height and that the launch angle corresponding to maximum range can be obtained by solving a transcendental equation. When launched at a critical angle, the projectile will return to its starting position. It turns out that the range and maximum horizontal displacement are not always equal. ![]() We solved the wind-influenced projectile motion problem with the same initial and final heights and obtained exact analytical expressions for the shape of the trajectory, range, maximum height, time of flight, time of ascent, and time of descent with the help of the Lambert W function.
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