Project 1 – Curve Fitting
In a wind tunnel experiment, the force on a projectile due to air resistance was measured at different velocities, according to the table below.
Velocity, t (100 ft/sec) 0 2 4 6 8 10 Force,p(t) (100 lb) 0 2.9 14.8 39.6 74.3 119
Follow the indicated steps to find an interpolating polynomial for these data that is a polynomial whose graph passes through the data points given in the table.
Use the function A(t) = a0 + a + a 2t2 + a 3t3 + a 4t4 + a sts
(a) Make a plot of the data.
(b) Find the system of equations with variables a0,…, a5 that results when the values for the velocity are substituted in for t in the function above.
(c) Write down the augmented matrix that corresponds to the system.
(d) Solve the system of equations. Determine if the system is consistent or not. If it is consistent, determine if the system has a unique solution or infinitely many solutions.
(e) Find the interpolating polynomial, if it exists.
(F) Graph the polynomial on your plot from part (a).
(g) Estimate the force on the projectile when it is traveling at 750 ft/sec. (Note the units in the table above.)