The falling object has a speed vo 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$$v$-$k$2$ y$,$ where v is the particle speed in inches per second, y is the penetration depth in inches, and k$$ and k$$ 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$=13$ sec$,$ k$230$ sec $2,$ and vo $=35$ in$./$sec$.$ After you have the plots, answer the questions as a check on your work.

Questons:

When t$=0\mathrm{.}19$ sec$,$

y$=$i

in$.,$

v $=1$

in$./$sec

When t $=0\mathrm{.}48$ sec$,$

y$=$ i

in$.,$

v$=$ i

in$./$sec

The object reaches $86\%$ of its final penetration distance when t$=$