With a little trigonometry anyone can figure out where a projectile is headed, how long it will take to get there, and what trajectory it will take. Consider a projectile to be an object that receives an initial force, but that is not self-powered. Think thrown or hit ball, shot cannonball, or sling-shot pebble, not airplane or rocket.
Now think graph. Vertical component y and horizontal component x. Add gravity (9.8 m/sec/sec). Oh, yes, you’ll need the initial velocity and the angle of inclination from that x axis. That’s about it. That’s all you need. With that info and a little trig, you can figure the height the projectile will reach, the time of its travel, and its travel distance. Math can make some seemingly complex things relatively simple. This might be of no interest to you unless you are a military gunner who wants to know if his howitzer will land a shell on the head of an enemy. Or, it might interest you if you want to figure whether the range of a shortstop allows him or her to reach a ball hit into the shallow outfield. Take the latter as an example. If the shortstop runs at a known rate and the ball is hit a known distance in a known time, can the player reach the ball before it hits the ground? Will the shortstop be too slow to arrive at the ball’s eventual destination? Will he or she make the catch on a ball hit between the infielders and outfielders?
Sometimes you are that shortstop. You have certain gifts and skills that might enable you to intercept something before it reaches its destination. Sometimes you’re just not fast enough to keep the ball from hitting the ground; at other times the ball is hit beyond your reach. That’s the way it is with an addicted person you want to help or with a problem that comes your way. The initial velocity of a person headed toward some personal harmful destiny isn’t easy to know. Addiction is a process, so we don't always recognize the initial velocity. “Oh! Let’s just try this stuff to see what it’s like.” The same goes for problems headed our way. Knowing that initial velocity is often impossible. Once the ball is in flight, however, concerned people need to react like the shortstop. Otherwise, the ball will land in the area beyond the infield but too shallow for the outfielders to catch. For the most part, we see the flight of the ball only after it comes off the bat, and we have to do a bunch of rapid calculating to catch it in time—that is, if we have the skill, time, and the energy to catch it.
Not everyone can be a good shortstop, but even the good shortstops can’t catch every ball before it crashes into the turf. Every shortstop is at a disadvantage. Each tries to position himself or herself to anticipate where a batter might, by habit, hit the ball. Yet, no one can know where the ball will land when it first comes off the bat. It’s only in response to a batted ball that shortstops can act. Sometimes, even when the player tracks the projectile correctly, a problem arises: The projectile hides in the sun or in the multicolored shirts of the crowd. Or the shortstop stumbles.
You can’t catch every ball, and you can’t intercept the fall of every addict or stop every problem from impacting. You can try, however, and you might, if you don’t make the catch, at least recover the ball after the first bounce. Good shortstops keep after the ball, even the balls that they miss. Good shortstops never give up. They sometimes make spectacular plays on balls that others might stop chasing after that initial impact.
Now think graph. Vertical component y and horizontal component x. Add gravity (9.8 m/sec/sec). Oh, yes, you’ll need the initial velocity and the angle of inclination from that x axis. That’s about it. That’s all you need. With that info and a little trig, you can figure the height the projectile will reach, the time of its travel, and its travel distance. Math can make some seemingly complex things relatively simple. This might be of no interest to you unless you are a military gunner who wants to know if his howitzer will land a shell on the head of an enemy. Or, it might interest you if you want to figure whether the range of a shortstop allows him or her to reach a ball hit into the shallow outfield. Take the latter as an example. If the shortstop runs at a known rate and the ball is hit a known distance in a known time, can the player reach the ball before it hits the ground? Will the shortstop be too slow to arrive at the ball’s eventual destination? Will he or she make the catch on a ball hit between the infielders and outfielders?
Sometimes you are that shortstop. You have certain gifts and skills that might enable you to intercept something before it reaches its destination. Sometimes you’re just not fast enough to keep the ball from hitting the ground; at other times the ball is hit beyond your reach. That’s the way it is with an addicted person you want to help or with a problem that comes your way. The initial velocity of a person headed toward some personal harmful destiny isn’t easy to know. Addiction is a process, so we don't always recognize the initial velocity. “Oh! Let’s just try this stuff to see what it’s like.” The same goes for problems headed our way. Knowing that initial velocity is often impossible. Once the ball is in flight, however, concerned people need to react like the shortstop. Otherwise, the ball will land in the area beyond the infield but too shallow for the outfielders to catch. For the most part, we see the flight of the ball only after it comes off the bat, and we have to do a bunch of rapid calculating to catch it in time—that is, if we have the skill, time, and the energy to catch it.
Not everyone can be a good shortstop, but even the good shortstops can’t catch every ball before it crashes into the turf. Every shortstop is at a disadvantage. Each tries to position himself or herself to anticipate where a batter might, by habit, hit the ball. Yet, no one can know where the ball will land when it first comes off the bat. It’s only in response to a batted ball that shortstops can act. Sometimes, even when the player tracks the projectile correctly, a problem arises: The projectile hides in the sun or in the multicolored shirts of the crowd. Or the shortstop stumbles.
You can’t catch every ball, and you can’t intercept the fall of every addict or stop every problem from impacting. You can try, however, and you might, if you don’t make the catch, at least recover the ball after the first bounce. Good shortstops keep after the ball, even the balls that they miss. Good shortstops never give up. They sometimes make spectacular plays on balls that others might stop chasing after that initial impact.
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