Problem Number $1(10$ pts$)$ A parachutist jumps at an altitude of $3000$ meters. If the parachute does not open, she is expected to approach a terminal speed of $30$ m$/$sec$.($g $=10$ m$/$s$2)($a$)[4$ points$]$ Assuming that air resistance is proportional to speed, about how long does it take her to reach $90\%$ of the terminal speed? $($b$)[2$ points$]$ How far has she traveled in reaching $90\%$ of the terminal speed? After her parachute opens, her speed is slowed to $3$m$/$sec$.$ As she hits the ground, she flexes her knees to absorb the shock. $($c$)[4$ points$]$ How far must she bend her knees in order to experience deceleration no greater than $10$ g$?$ Assume that her knees are like a spring with a resisting force proportional to displacement $($mechanical energy is conserved$).$