Chapter 3.4, Problem 8E

Unless otherwise stated, in the following problems we assume that the gravitational force is constant with $g=9.81{\text{m/sec}}^{\text{2}}$ in the MKS system and $g=32{\text{ft/sec}}^{\text{2}}$ in the U.S. Customary system.

A parachutist whose mass is $100\text{ kg}$ drops from a helicopter hovering $3000\text{m}$ above the ground and falls 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 $b_3=\text{20}\text{N-sec/m}$ when the chute is closed and $b_4=100\text{N-sec/m}$ when the chute is open. If the chute does not open until 30 sec after the parachutist leaves the helicopter, after how many seconds will he hit the ground? If the chute does not open until $1\text{ min}$ after he leaves the helicopter, after how many seconds will he hit the ground?