if you want To be a pitcher in Major League Baseball, you must be able to throw the ball TRUE It’s about 85 to 160 miles per hour. The faster the pitch, the less time the batter has to react and swing the bat, and the more likely he is to hit the ball and score a strike. (For non-baseball fans: A strike is when the batter misses or misses the ball by swinging it in the strike zone. Of course, 3 strikes and you’re out.) This requirement has a lot of meaning. The dream of being a pitcher in the major leagues was crushed.
But… is it possible to throw a strike at a slower speed?
In fact, a significant number of players are throwing strikes at very low velocity, reaching as high as 51.1 mph in one case. coded baseball Twitter account. When the game goes into overtime and the team runs out of relief pitchers, the manager may send position players to the mound. Non-regular pitchers typically throw the ball at a slow speed, but can still score strikes.
Let’s use Python to model some pitches and see how difficult this is.
fast pitch trajectory
As the ball leaves the pitcher’s hand, it travels along a path governed by two forces: gravity, which pulls it downwards, and air resistance, which pushes it backwards. The combination of these two forces changes the speed of the ball as it travels towards home plate.
Gravity is a constant force that depends only on the ball’s mass (approximately 0.144 kilograms) and the gravitational field (g = 9.8 Newtons/kg), so it’s fairly easy to deal with. Drag is more difficult because the magnitude and direction of this force depend on the velocity of the ball. The problem is that the net force changes the velocity of the ball, but now one of those forces (drag) changes. depends About ball speed.
Almost the only way to model this motion is with numerical calculations that divide the motion into small time intervals. The force can be assumed constant during each of these intervals. If you keep the force constant, you can see how the baseball’s velocity and position change. In the next time interval, the velocity has changed, so we can find a new force and repeat the whole process.
This may seem like a “physics cheat”, but there are countless problems that can only be handled this way. My favorite example is solving the three-body problem (which governs, for example, the interaction of three stars in the universe). Modeling the Earth’s Climateor model the quantum mechanics of atoms other than hydrogen.
Before we do that, let me answer two frequently asked questions. First, do we really need to include air resistance?
