3. In a wind tunnel experiment, the force on a projectile due to the air resistance was measured at different velocities: Velocity 0 2 4 6 8 10 Force 0 2.90 14.8 39.6 74.3 119 (a) Find an interpolating polynomial p(t) = a + a₁t + at² + azt³ + ast¹ + ast³. (That is, find the coefficients a0, a1,... of such a polynomial, so that p(0) = 0, p(2) = 2.90, p(4) 14.8,...). Do NOT use any regression/polynomial/polyfit fitting tools to solve this problem. Rather, solve this problem using techniques from linear algebra by formulating this problem as a system of equations that can be expressed as Ar = 6, where is the vector of coefficients do...., as you are trying to find, and 5 is the vector of the output (force) values. Matrix A is the coefficient matrix. As a hint, this question is similar to the problem that was assigned in Section 1.2, #33. (b) Plot your result p(t) with the data. (c) What happens if you try to use a polynomial of degree less than 5? For example, try using a polynomial of degree 3. Explain your answer.