Juggling Simulation: Investigating the Relationship Between X & Y Velocity

[Meowzers]

Hi, I am working with a juggling simulation to better my understanding of projectile motion. However, I encountered a slight problem.

To my understanding, an initial y velocity and an initial x velocity are independent of each other. A y-velocity affects the height of how high the ball travels in the air whereas the x-velocity affects the horizontal displacement of the ball (to the other hand of the juggler).

So, let's say I want the ball to be juggled higher, why does it seem to also affect the x-velocity (as I observed in the simulation) when it's supposed to be independent of the height (y-axis)? The higher inital y-velocity I input, the higher the ball goes. So why does the inital x-velocity need to decrease? Isn't it supposed to stay the same?

 

[SGT]

Velocity is a vector. In your case it is decomposed in x and y components. If the modulus of your vector is constant, increasing one component will decrease the other.

 

[kyle8921]

Thank you for sharing your findings from your juggling simulation. I would like to offer some insights and explanations for the observed relationship between x and y velocity.

Firstly, it is important to note that while x and y velocity are independent of each other, they are still both affected by the same external force of gravity. This means that any changes in one velocity can impact the other, as they are both influenced by the same force.

In the case of juggling, the initial y velocity is directly related to the height of the ball's trajectory. As you mentioned, a higher initial y velocity will result in a higher maximum height for the ball. However, this also means that the ball will spend more time in the air, increasing the time it takes to travel horizontally.

This is where the relationship between x and y velocity becomes apparent. As the ball spends more time in the air due to a higher initial y velocity, the x velocity must decrease in order for the ball to reach the other hand of the juggler. This is because the horizontal displacement is dependent on the time of flight of the ball, which is affected by the initial y velocity.

In other words, the decrease in x velocity is necessary to compensate for the longer time in the air caused by the higher y velocity, in order for the ball to reach the other hand at the desired height.

I hope this explanation helps to clarify the relationship between x and y velocity in the context of juggling. It is important to remember that while these velocities are independent, they are still both influenced by the same external force and can affect each other in certain scenarios.