$($b$)$ In a wind tunnel experiment, the force on a projectile due to air resistance was measured at different velocities:

$[$Velocity $(100f\frac{t}{sec}),0,2,4,6,8]$

$[$Force $(100lb),0,2\mathrm{.}90,14\mathrm{.}8,39\mathrm{.}6,74\mathrm{.}3]$

$($i$)$ Find an interpolating polynomial for these data using MATLAB.

Use $p(t)=a_0+a_{1}t+a_2{t}^2+a_3{t}^3+a_4{t}^4$

$($ii$)$ Plot the solution curve in MATLAB.

$($iii$)$ Estimate the force on the projectile when the projectile is traveling at $650f\frac{t}{sec}.$

$($iv$)$ What happens if you try to use a polynomial of degree less than $4?($Try a cubic polynomial $p(t)=a_0+a_{1}t+a_2{t}^2+a_3{t}^3,$ for instance.$)$