# Projectile Motion and Volleyball!

## What is Projectile Motion ? ? ?

During the kinematics unit in physics class, we learned about projectile motion. Projectile motion is when a projectile is launched or shot at an angle. For projectile motion at an angle, velocity of the horizontal component is constant, and velocity of the vertical component increases and decreases due to gravity. Gravity causes the acceleration of a object in projectile motion. There is also an horizontal and vertical component for distance. The vertical height would be how high a projectile reaches at a certain time, and the horizontal height would be how far from the original position the projectile has landed.

Also, all objects accelerate due to gravity, and this affects the projectile's motion. In projectile motion at an angle, the gravity (acceleration) is always...  This diagram shows an example of Projectile Motion and the Velocity Vectors. The "Vx" (horizontal component of velocity) vector is shown as constant by staying the same size and direction throughout the motion of the projectile. It is also clear the the "Vy" (vertical component of velocity) decreases to zero at the highest point, and increases as the projectile begins to fall.

## Volleyball ## Serving a Volleyball

In volleyball, the most important part is the serve. Without the serve, the game would never start. This makes a serve pretty important right? Not to mention, the ball must land in the court of the opposing side, and it must make it over the 2.24 meter net. Each side of the court is 9 by 9 meters. A server must stand at the end line of their side. Therefore, the serve must travel 9 meters to make it to the other side, and then must land anywhere in the 9 by 9 meters square of the other side. The player contacts the ball at the highest point possible (therefore their hand is extended straight). Good players also try to serve with the least amount of vertical height as possible (so that the serve barely clears the height of the net).

## Volleyball is a Projectile Motion ? ? ? ## Is Serving a Volleyball a Projectile Motion ? ? ?

Yes! Serving a ball looks just like the person in the picture above, and the motion of the ball is similar to the projectile motion diagram above.

If you think about it, a volleyball player tosses the ball in the air, and hits it in front of them. Their arm hitting the ball causes the ball to "launch" over the net to the other side. The ball is therefore given an initial velocity at an angle. ## My Question

How can the principles of projectile motion help you to serve the volleyball in the court?

## Scenario...

First of all, all air resistance will be neglected. Second, I want to figure out if my knowledge of projectile motion can help volleyball players serve the ball in the court.

I am going to say that I want a ball served exactly on the end line of the other team's court. This means that the ball will travel 18 meters. So, we know that our horizontal distance is 18 meters.

• x= 18 m
I want to find out how projectile motion can help me to make sure the ball lands inside the court. I am going to find out what my initial velocities and heights need to be for a ball that is served in...

• 1 s
• 1.5 s
• 2 s
• 2.5 s

We are also going to say that the height of where the ball is contacted (on the serve) is the same height at which a defender passes it. This makes the projectile symmetric, meaning the time it takes to reach the maximum height will be the same on it's way down. In this case, we don't really have to worry about the height of the net since most volleyball players are as tall as the net when their hand is straight up.

## Equations

In all of the equations, Vf means the same as Vo, because since a projectile motion is symmetrical, the initial and final velocities will be the same. For the ball to only take 1 second to go 18 meters, it is almost a horizontal projectile. This means the ball almost traveled in a straight line. But, since the angle is 15.2 degrees, we know that it is still a projectile at an angle. This serve also has a high initial velocity, because the ball has to be going fast for it to only take 1 second. The angle at which the ball must be fired for it to take 1.5 seconds to be served doubles from the angle of a serve that takes 1 second. I predict that the more seconds the serve takes, the angle at which the ball is served will increase. Also, the initial velocity decreases. This means that the ball still must be served with a high initial velocity, but it also means that the ball have a higher maximum height the longer it is in the air. As predicted, the angle increased, and the maximum height will too. I know this all because of the angle at which the ball is fired. The higher the angle, the higher the projectile will go. Also similar to the previous equations, the velocity has continued to decrease. I expected this, because the longer the ball is in the air, the slower the ball must be going right??? Once again, the angle increased. But, something different happened. The velocity needed for the serve to make it 18 meters increased. I took me a while to understand why, but I do now. Since the angle has been increasing, the maximum height of the ball has been increasing too. The ball needs a high initial velocity if it is fired at the angle seen above.

## SO... How can the information help me serve the ball in the court ? ? ?

First of all, I learned that in all of these cases, the maximum height that my ball will reach must be right over the net. I say this because projectile motions are symmetrical. This means that both halves of the trip are the same for the projectile. That is also why I could could find the initial velocity of the y-component my multiplying half the time by the acceleration (gravity). I also learned that if I want to serve a ball that goes really high, that I also must serve the ball with a high initial velocity, otherwise it wouldn't make it all 18 meters. All this information will help me because after doing all this research and equations, I can now apply kinematics and my knowledge of projectile motion on the volleyball court!!!!! Thank you physics!!!!!