The falling object has a speed $v_0$ when it strikes and subsequently deforms the foam arresting material until it comes to rest. The resistance of the foam material to deformation is a function of penetration depth $y$ and object speed $v$ so that the acceleration of the object is $a=g-k_{1}v-k_{2}y,$ where $v$ is the particle speed in inches per second, $y$ is the penetration depth in inches, and $k_1$ and $k_2$ are positive constants. Plot the penetration depth $y$ and velocity $v$ of the objects as functions of time over the first five seconds for $k_1=13se{c}^{-1},k_2=23se{c}^{-2},$ and $v_0=40in\frac{.}{sec}.$ After you have the plots, answer the questions as a check on your work.

Questons:

When $t=0\mathrm{.}27sec,y=$ in$.,,v=$ in$.\frac{?}{sec}$

When $t=0\mathrm{.}71sec,y=$ in$.,,v=$ in$./$sec The object reaches $87\%$ of its final penetration distance when $t=$ sec$.$