Professor of Mathematics Robert Kantrowitz '82 was the colloquium speaker at LeMoyne College's Mathematics Department in Syracuse on April 15. In his talk, "Golf, tee ball, and triangles," Kantrowitz compared various solutions to the problem of determining the angle of launch that maximizes the range of a projectile released from above ground level and landing on a hill. These included different approaches from calculus alongside solutions provided by the computer algebra system Maple. The talk concluded with a look at geometric properties of the optimal launch angle.
Ball players of all varieties should take note of this presentation. Golfers and kickball players should hit or kick a ball that is resting on level ground at a 45-degree angle to gain maximal range. This is a classical result, apparently known to Galileo.
For tee ball players who are hitting from above ground level -- or for someone trying to throw an object out of a high window as far as possible -- a 45-degree angle is, in fact, not optimal. Rather, as the launch point gets higher and higher, calculus confirms that the angle that will achieve maximal range decreases.
If the playing field is literally not level, that is, if a golfer, or kicker, or tee ball batter is hitting or kicking down a hill, for example, adjustments need to be made in the launch angle as well; here, too, the best angle is not 45 degrees, but gets closer and closer to 0, as the hill slopes more and more downward.
Ball players of all varieties should take note of this presentation. Golfers and kickball players should hit or kick a ball that is resting on level ground at a 45-degree angle to gain maximal range. This is a classical result, apparently known to Galileo.
For tee ball players who are hitting from above ground level -- or for someone trying to throw an object out of a high window as far as possible -- a 45-degree angle is, in fact, not optimal. Rather, as the launch point gets higher and higher, calculus confirms that the angle that will achieve maximal range decreases.
If the playing field is literally not level, that is, if a golfer, or kicker, or tee ball batter is hitting or kicking down a hill, for example, adjustments need to be made in the launch angle as well; here, too, the best angle is not 45 degrees, but gets closer and closer to 0, as the hill slopes more and more downward.
