Question

In a wind tunnel experiment, the force on a projectile due to the air resistance was measured at different velocities:
Velocity (100 ft/sec) 0 2 4 6 8 10
Force (100 lb) 0 2.90 14.8 39.6 74.3 119
Find an interpolating polynomial p(t) = a0 + a1t + a2t 2 + a3t 3 + a4t 4 + a5t 5 for these data (that is, find the coefficients a0, a1, .... of such a polynomial, so that p(0) = 0, p(2) = 2.90, p(4) = 14.8...).
What happens if you try to use a polynomial of degree less than 5?

Answer 1

Answer:

  see below

Step-by-step explanation:

A graphing calculator can be a suitable tool for curve fitting. The attachment shows the coefficients a5 ... a1 for a 5th-degree interpolating polynomial. The coefficient a0 is 0, because the y-intercept is zero.

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When a lower-degree polynomial is used, the fit is not exact at every point.

The table in the attachment shows the interpolated values for a 3rd-degree interpolating polynomial in the right-most column.