How to get the equation for 3D projectile motion?

AI Thread Summary
The discussion focuses on modeling the trajectory of a tennis ball in 3D for a math exploration paper, using initial conditions like velocity, height, and angles. The user seeks to create equations in Geogebra while excluding factors like spin, drag, and air resistance, which are crucial for accuracy. Concerns are raised about the simplification of these factors, suggesting that including them would enhance the model's validity. The conversation also prompts the user to clarify the specific problem statement and the academic level of the class involved. Ultimately, the goal is to derive a comprehensive equation for the ball's motion under the influence of gravity alone.
PlasmaRadiator24
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Hey guys, so I'm currently writing a math exploration paper on modelling the optimal tennis serve. I am using Geogebra and I was wondering if you could help me come up with the equation that will help model the trajectory of the tennis ball over time given the following conditions:
1. Initial Velocity
2. Initial Height
3. Initial vertical angle
4. Initial Horizontal angle

I would like to model this on a 3 dimensional plane meaning (x,y,z) this is where i have an issue.
I decided to exclude the spin, drag, and air resistance as any factors involved. The only force acting on the ball after the serve is ag at 9.8m/s^2.
 
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PlasmaRadiator24 said:
Hey guys, so I'm currently writing a math exploration paper on modelling the optimal tennis serve. I am using Geogebra and I was wondering if you could help me come up with the equation that will help model the trajectory of the tennis ball over time given the following conditions:
1. Initial Velocity
2. Initial Height
3. Initial vertical angle
4. Initial Horizontal angle

I would like to model this on a 3 dimensional plane meaning (x,y,z) this is where i have an issue.
I decided to exclude the spin, drag, and air resistance as any factors involved. The only force acting on the ball after the serve is ag at 9.8m/s^2.
Welcome to the PF. I've deleted several cross-posts of yours.

Ignoring air resistance and spin seems to be a fundamental error of simplification. Those are fundamental to a good tennis serve. Can you comment about including those effects?
 
I suppose that it would make my model much more accurate, however what I am worried about is the complexity of finding all the equations relating all these factors. The images below show my initial modelling of the tennis court and now the problem is getting the equations to move the ball according to the factors above to model the balls's trajection.
 

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What class is this for? If it's for anything beyond a non-calculus first physics clsss, it would seem that air resistance and the effects of spin would be key.

Part of the Homework Help Template that you deleted asks for the exact problem statement in full. Can you please provide that, and say which uni class this problem is for?
 

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