Parabolic Equation assistance please.

  • Thread starter GregD603
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In summary, the Parabolic Equation, y = tan(θ)x - (g / 2vo²cos²θ), can be obtained by substituting t = x/Vxo into the kinematic equations of motion for constant acceleration. This allows for finding the vertical position at any horizontal position for a given angle and initial velocity. The equation can be rewritten as y = (tanΘo)x - (g/2V2ocos2Θo)x2, where V2o is the initial velocity squared. LaTex is used to format mathematical equations in a clearer and more readable way.
  • #1
GregD603
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I've been having difficulty understanding how the Parabolic Equation works... everytime I do a problem I get some really nasty looking numbers and often times it just doesn't work at all.
The equation I was taught is:

y = tan(θ)x - ( g / 2vo²cos²θ ) where vo = initial velocity vector

This equation was derived from: x = VxoT -or- T = x / Vxo (T = time) and
y = VyoT - ½gt²

Please help me understand how to apply this formula correctly.

Thank you very much,
Greg from Mass.
p.s. I know I didn't answer part three of the Template, however my question is more conceptual based rather than example. Pls don't delete
 
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  • #2
Well for a given angle and initial velocity, you can find the vertical position at any horizontal position. I'm not too really sure what kind of answer you are looking for.
 
  • #3
GregD603 said:
I've been having difficulty understanding how the Parabolic Equation works... everytime I do a problem I get some really nasty looking numbers and often times it just doesn't work at all.
The equation I was taught is:

y = tan(θ)x - ( g / 2vo²cos²θ ) where vo = initial velocity vector

This equation was derived from: x = VxoT -or- T = x / Vxo (T = time) and
y = VyoT - ½gt²

Please help me understand how to apply this formula correctly.

Thank you very much,
Greg from Mass.
p.s. I know I didn't answer part three of the Template, however my question is more conceptual based rather than example. Pls don't delete

Welcome to the PF, Greg. I'm not seeing where your top equation comes from. The bottom ones appear to be the kinematic equations of motion for constant acceleration (the "g" in this case), although they are a bit difficult to read without using LaTex:

[tex]y(t) = y_0 - \frac{1}{2} gt^2[/tex]

How did you go from the kinematic equations to your first equation?
 
  • #4
Thanks for the responses so quickly. And I"m sorry but I don't know what LaTex is, or where to obtain it. :(

My textbook tends to be super confusing about stuff that should be pretty simple, I guess.
The way it's described is:

t = x/Vxo is substituted into y = VyoT - ½gt² to obtain
y = Vyo(x/Vxo) - ½g(x/Vxo)² which can be rewritten as
y = (Vyo/Vxo)x - (g/2v2ocos2Θo)x2 or
y = (tanΘo)x - (g/2V2ocos2Θo)x2

and V2o is supposed to be initial velocity V squared.
 

1. What is a parabolic equation?

A parabolic equation is a mathematical expression that describes a parabola, which is a U-shaped curve. It is typically written in the form y = ax^2 + bx + c, where a, b, and c are constants.

2. How is a parabolic equation used in science?

Parabolic equations are used in various fields of science, such as physics, engineering, and astronomy. They can describe the motion of projectiles, the shape of satellite dishes, and the path of light in lenses, among other things.

3. What is the significance of the coefficients in a parabolic equation?

The coefficient a determines the steepness of the parabola, with larger values resulting in a narrower curve. The coefficient b affects the position of the parabola on the x-axis, while c determines the vertical position of the parabola on the y-axis.

4. How can I graph a parabolic equation?

To graph a parabolic equation, plot several points on the coordinate plane using different values for x. Then, connect the points with a smooth curve. Alternatively, you can use a graphing calculator or software to quickly graph the equation.

5. Are there any real-world applications of parabolic equations?

Yes, there are many real-world applications of parabolic equations. For example, they are used in designing roller coasters, predicting the trajectory of a thrown ball, and analyzing the shape of bridges and arches. They also have applications in economics, biology, and other fields.

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