Problems Part $1$

Instead of using $\backslash$Delta $\backslash$Delta $$

$,$ you can use the numpy polyfit to determine the acceleration of the ball.

a$.$ Use your coordinates from the saved $.$npz file you used above to load your projectile motion data

npz$\_$coords $=$ np$.$load$(\text{'}$projectile$\_$coords.npz$\text{'})$

t $=$ npz$\_$coords$[\text{'}$t$\text{'}]$

x $=$ npz$\_$coords$[\text{'}$x$\text{'}]$

y $=$ npz$\_$coords$[\text{'}$y$\text{'}]$

b$.$ Calculate $$

and $$

using a finite difference again, then do a first$-$order polyfit to $$

and $$

vs $$

$.$ What is the acceleration now?

c$.$ Now, use a second$-$order polynomial fit for x$-$ and y$-$ vs t$.$ What is acceleration now?

d$.$ Plot the polyfit lines for velocity and position $(2$ figures$)$ with the finite difference velocity data points and positions. Which lines look like better e$.$g$.$ which line fits the data?