You bail out of a helicopter and pull the ripcord of your parachute. Now the air resistance proportionality constant is k=1.57, so your downward velocity satisfies the initial value problem below, where v is measured in ft/s and t in seconds. In order to investigate your chances of survival, construct a slope field for this differential equation and sketch the appropriate solution curve. What will your limiting velocity be? Will a strategically located haystack do any good? How long will it take you to reach 95% of your limiting velocity.
dv/dt=32-1.57v, v(0)=0
