Finding length of an arc produced by projectile

In summary, the conversation discusses the approach of finding a general formula for fun and specifically, the arc length of a parabola. The speaker, a high school student, expresses difficulty with calculus and shares their current approach of finding y as a function of x and using the arc length formula. They also mention their doubts about the correctness of their formula and their limited knowledge of calculus. They inquire if there is a better approach and ask for the correct formula. The conversation ends with a suggestion to post their work as homework and a reminder that arc length questions are best posed as math questions, not physics.
  • #1
sk0071
1
0
So I decided to try deriving a general formula for fun. Being a high school student, the calculus got scary very fast. At this point, I'm just curious as to what the best approach to this might be. The approach I used was finding y as a function of x and then inputting it into the arc length formula. I eventually derived a very complicated formula that I think is wrong. I don't know very much about calculus as everything I've learned about it I've learned through the internet. Would this approach work? Is there a better way? If so what is the correct formula?
 
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  • #2
You should post what you've done as homework. It's not possible to help without seeing what you've done.
 
  • #3
Arc length question is best posed as a math question - not physics.
 
  • #4

Related to Finding length of an arc produced by projectile

What is the formula for finding the length of an arc produced by a projectile?

The formula for finding the length of an arc produced by a projectile is:
L = R * θ, where L is the length of the arc, R is the radius of the circle, and θ is the central angle subtending the arc.

How do you calculate the central angle of an arc produced by a projectile?

The central angle can be calculated using the formula:
θ = arctan(v₀²sin²α / gR), where v₀ is the initial velocity of the projectile, α is the angle of projection, g is the acceleration due to gravity, and R is the radius of the circle.

Can the length of an arc produced by a projectile be negative?

No, the length of an arc produced by a projectile cannot be negative. It is always a positive value representing the distance traveled by the projectile along the curved path.

What units should be used when finding the length of an arc produced by a projectile?

The length of an arc produced by a projectile is typically measured in the same units as the radius of the circle, such as meters or feet. However, it is important to maintain consistency and use the same units for all values in the formula.

Is there a difference in finding the length of an arc produced by a projectile in different coordinate systems?

Yes, the length of an arc produced by a projectile can vary depending on the coordinate system used. In a Cartesian coordinate system, the length can be found using the formula mentioned above. In a polar coordinate system, it can be calculated using the formula:
L = R * Δθ, where Δθ is the change in angular displacement from the initial position to the final position of the projectile.

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