Flight of Bird, Cubic Function

In summary, the conversation discusses finding a cubic equation to model the estimated flight of a bird, which dove under water and re-emerged with a fish. Two unknown variables, a and k, are introduced and the process of substituting points into the equation is discussed. The solution involves finding two equations with two unknowns and potentially using least squares fitting. The level of math being discussed is not specified.
  • #1
CR7
1
0

Homework Statement



A bird dove under water and re-emerged with a fish. Following is the table which shows the bird's estimated flight:

Time(s),Height(m)
0, 7
2, 10
4, 5
6, 0
7, 0
8, 3

Find a cubic equation to model the data.

2. The attempt at a solution

y=a(x-6)(x-7)(x-k) a,k are both unknown variables

5=a(4-6)(4-7)(4-k) Substituted any 2 points from the table above

5=a(-2)(-3)(4-k)

5=6a(4-k)

Not sure how to solve because there are 2 unknowns. Am I on the right track?
 
Physics news on Phys.org
  • #2
You really only substituted 1 point, defined by two values (t, h).

Try substituting one more different point into the original, then you'll have two equations with two unknowns.
 
  • #3
@cr7: What level of math are you taking? Are you given that the points come from a cubic so a cubic through any 4 points will automatically fit the others? Or have you studied least squares fitting? Of course, if the points are exactly from a cubic, least squares fit will give it too.
 

1. What is the "Flight of Bird, Cubic Function"?

The "Flight of Bird, Cubic Function" is a mathematical model that describes the trajectory of a bird in flight as it flaps its wings. It is based on the cubic function, which is a type of polynomial with a degree of 3.

2. How is the "Flight of Bird, Cubic Function" different from other flight models?

The "Flight of Bird, Cubic Function" takes into account the flapping motion of a bird's wings, whereas other flight models may only consider the bird's overall movement through the air. This makes it a more accurate representation of a bird's flight.

3. What factors determine the shape of the "Flight of Bird, Cubic Function"?

The shape of the "Flight of Bird, Cubic Function" is determined by several factors, including the bird's wingspan, the frequency and amplitude of its wing flapping, and the air resistance it encounters during flight. These factors can vary between different bird species and even within the same species.

4. How is the "Flight of Bird, Cubic Function" used in scientific research?

The "Flight of Bird, Cubic Function" is used in scientific research to better understand the flight patterns and capabilities of different bird species. It can also be used to design more efficient flying robots and to study the effects of environmental factors on bird flight.

5. Can the "Flight of Bird, Cubic Function" be applied to other animals or objects?

While the "Flight of Bird, Cubic Function" was originally developed for bird flight, it can potentially be applied to other animals or objects that exhibit a similar flapping motion, such as bats or flying insects. However, the specific parameters of the function would need to be adjusted to fit the characteristics of the particular animal or object being studied.

Similar threads

  • Precalculus Mathematics Homework Help
Replies
4
Views
946
  • Precalculus Mathematics Homework Help
Replies
7
Views
1K
  • Precalculus Mathematics Homework Help
Replies
3
Views
1K
  • Precalculus Mathematics Homework Help
Replies
7
Views
2K
  • Precalculus Mathematics Homework Help
Replies
3
Views
804
  • Precalculus Mathematics Homework Help
Replies
3
Views
281
  • Precalculus Mathematics Homework Help
Replies
6
Views
835
  • Precalculus Mathematics Homework Help
Replies
6
Views
1K
  • Precalculus Mathematics Homework Help
Replies
1
Views
1K
  • Precalculus Mathematics Homework Help
Replies
4
Views
747
Back
Top