Hi guys, it's Gokul, the techie at the Tellury. So I'm going to have to write the sports article for this week. However, since the only sport I know anything about is swimming, and nothing interesting ever happens in swimming, I've decided to talk about baseball. Specifically, how far can I throw a baseball. To make this simple, we will assume we are in only 2 dimensions and their is no air resistance. We will also assume that you are somewhere between 14-15 and are of the average height for that age(65 in). For those of you who have had a little physics, you will know we are doing a classic projectile motion problem. You would also know that a 45 degree angle is the best angle to throw a ball for distance because of how throws at complementary angles travel the same distance.[diagram]This is because of how 45 degrees acts as a sort of "mirror" in the center of the 0-90 degree spectrum. If you don't believe me, try reading this: Freefall Physics .
So now we have the angle we are going to throw it at and your height. But now we need to know how fast you can throw it. According to Yahoo answers, which is always a reliable source, the average high school freshman can pitch at 60 mph. But that's at perfectly horizontal angle. For those of you who have had a little bit of geometry, you know the sine of angle is the ratio of the opposite to the hypotenuse, and the cosine is the ratio of the adjacent side to the angle to the hypotenuse. One thing you will learn in physics that is really cool is velocity is a vector. Thus it it has horizontal and vertical components. So we can model it like a right triangle and no one can tell us we can't. SWAG. By using 45 as the angle and 60 mph as the speed, we get the vertical component as 26.8224 m/s and the horizontal as 26.8224 m/s. Remember that 45 degrees acts as a mirror and thus both sides are equal.
A few of you may know that the acceleration due to gravity is -9.81 m/s^2. You may also know that motion in two dimensions can be broken down into 2 one dimensional problem. To save you some time, I will do the math myself.
So all in all, the maximum distance a high-school freshman can pitch to is 149 meters. Notice how it is not dependent on the mass of the ball, only the speed. So if you could throw a basketball at 26 m/s, you could still throw more that 5 full NBA courts. For those of you who play baseball, check my estimate and post a response in the comments.
And as a final question, what angle should I throw it at to get the highest speed possible. Leave your angle in the comment section below, and a Merry Christmas to all(political corectness has no use to physicists).
A few of you may know that the acceleration due to gravity is -9.81 m/s^2. You may also know that motion in two dimensions can be broken down into 2 one dimensional problem. To save you some time, I will do the math myself.
So all in all, the maximum distance a high-school freshman can pitch to is 149 meters. Notice how it is not dependent on the mass of the ball, only the speed. So if you could throw a basketball at 26 m/s, you could still throw more that 5 full NBA courts. For those of you who play baseball, check my estimate and post a response in the comments.
And as a final question, what angle should I throw it at to get the highest speed possible. Leave your angle in the comment section below, and a Merry Christmas to all(political corectness has no use to physicists).