A parachutist whose mass is

$80$

kg drops from a helicopter hovering

$2000$

m above the ground and falls toward the ground under the influence of gravity. Assume that the force due to air resistance is proportional to the velocity of the$$ parachutist, with the proportionality constant

b $1$equals$=30$

$$N$-$sec$/$m when the chute is closed and

b $2$equals$=90$

$$N$-$sec$/$m when the chute is open. If the chute does not open until the velocity of the parachutist reaches

$20$

$$m$/$sec$,$ after how many seconds will the parachutist reach the$$ ground? Assume that the acceleration due to gravity is

$9\mathrm{.}81$ m divided by sec squared$9\mathrm{.}81$m$/$sec$2.$