Linear Algebra help. =(!?

Question

A radar is tracking an object falling onto earth away from it, and three observations are successively recorded and given in
the following table:

[Horizontal distance (m) : 1 2 3 ]
[Vertical distance from earth : 1948 1860 1760 ]

Choosing the horizontal distance as input variable, use polynomial interpolation to estimate the horizontal disance of the object from the radar when it hits the ground.

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Now I would appreciate if you could tell me how I can do it?
I tried my textbook and I dont understand it, "find an equation that fits the data in the table" how? So please guide me through this question. Thanks

Thanks both of you, I understand =D It clicked in, not so hard after all. Thanks!

Answer 1

from 1 sec to 2 sec it traveled 88 (IE 1948-1860)
from 2sec to 3 sec it traveled 80 (IE 1860 - 1760)
... 80 expressed in relation to 88 is:
X - X/11

so you can estimate that the object is going to travel -1/11 as far (one eleventh LESS far) each second than it did the previous second.

Now that you understand the equation
the math becomes simple
using the knowledge that is travels 1/11 LESS per second than it did in the previous second (and using the given data as a "start" point) when (how many seconds) will it it take to hit the ground (vertical = 0)

Answer 2

With 3 data points, assume a quadratic relationship y = a + bx + cx^2
a + b + c = 1,948 (1)
a + 2b + 4c = 1,860 (2)
a + 3b + 9c = 1,760 (3)
Subtracting (2) from (3) and (1) from (2),
b + 5c = - 100 (4)
b + 3c = - 88 (5)
Subtracting (5) from (4),
2c = - 12
c = - 6
b = - 100 + 60 = - 40
a = 1,948 + 40 + 12 = 2,000
Now
- 6x^2 - 40x + 2000 = 0
3x^2 + 20x - 1000 = 0
x = (- 20 ± √(400 + 12,000))/6
x = (- 20 ± √12,400)/6
Since x must be positive,
x = (- 20 + √12,400)/6
x ≈ 15.22588 ≈ 15.22

Answer 3

The matrix version of the priority is AX = b the place A is a 2x2 matrix [4, ok; ok, a million] X is a vector variable [x; y] and b is a vector consistent [7; 0] there'll be a diverse answer as long as A is non-singular. there is merely not a diverse answer if A *is* singular. For A to be singular det(A) = 0 the place det() is the "determinant" of a sq. matrix for a 2x2 matrix [a, b; c, d] det([a, b; c, d]) = advert - bc consequently on your case 4*a million - ok*ok = 0 ok^2 = 4 ok = +/- 2