Problem $01\mathrm{.}002.$ Free$-$falling bungee jumper analytical solution with an initial velocity Consider the equation $\frac{dv}{dt}=g-\frac{a}{m}v|v|.$

Problem $01\mathrm{.}002$c c $-$ Free$-$falling bungee jumper analytical solution verification

A bungee jumper with a mass of $68\mathrm{.}1kg$ jumps upward from a stationary hot alr balloon. Use appropriate equations for vobtained in the previous questions to compute values of the velocity from $t=0$ to $12s$ at intervals of $2s.$ Use a drag coefficient of $0\mathrm{.}25k\frac{g}{m}$ with an upward initial velocity of $40\frac{m}{s}.$ Note that for this case, the zero velocity occurs at $t=3\mathrm{.}470239s.($Round the final answer's to five decimal places. Include a minus sign if necessary.$)$

The values are tabulated below.

$\backslash$table$[[$F$(5),K(\frac{m}{s})$