How to get the equation for 3D projectile motion?

In summary, the individual is seeking help with creating an equation to model the trajectory of a tennis ball after a serve, using the software Geogebra. They are looking for assistance with incorporating initial velocity, height, vertical and horizontal angle into a 3-dimensional plane. The individual is also considering excluding the effects of spin, drag, and air resistance in their model. However, it has been suggested that these factors are important to consider for a more accurate model. The individual is concerned about the complexity of finding equations for all the factors. This problem is part of a math exploration paper for a university class.
  • #1
PlasmaRadiator24
2
0
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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  • #2
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?
 
  • #3
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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  • #4
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?
 

1. How do you determine the initial velocity in the equation for 3D projectile motion?

The initial velocity in the equation for 3D projectile motion can be determined by using the formula: V0 = Vcosθ, where V is the initial velocity, θ is the angle of projection, and V0 is the initial horizontal velocity.

2. How is acceleration incorporated into the equation for 3D projectile motion?

Acceleration is incorporated into the equation for 3D projectile motion through the term -9.8t2, which represents the acceleration due to gravity. This term is added to the y-direction equation to account for the changing velocity and position of the projectile.

3. What is the significance of the angle of projection in the equation for 3D projectile motion?

The angle of projection in the equation for 3D projectile motion determines the initial direction of the projectile's motion. The angle affects both the horizontal and vertical components of the initial velocity, and can greatly impact the trajectory and range of the projectile.

4. How do you account for air resistance in the equation for 3D projectile motion?

Air resistance is often ignored in the equation for 3D projectile motion, as it can be difficult to accurately measure and account for in real-world situations. However, if necessary, air resistance can be incorporated into the equation by adding a drag term, which is dependent on the velocity and direction of the projectile.

5. What is the range equation for 3D projectile motion?

The range equation for 3D projectile motion is R = V02sin2θ/g, where R is the maximum horizontal distance traveled by the projectile, V0 is the initial velocity, θ is the angle of projection, and g is the acceleration due to gravity. This equation can be derived from the equations for the x and y components of the projectile's motion.

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