November 1996  ICTCM IX (Reno)  7

• Suppose that k/m = 0.2 before the skydiver opens the parachute. What is the terminal velocity for the free-falling skydiver?

• Suppose the airplane is 2000 m above the ground when the skydiver jumps out. What is the skydiver’s altitude [when the skydiver reaches 95 percent of the terminal velocity]?

• The coefficient of air resistance changes after the parachute opens. Suppose that the skydiver, who has reached a new terminal velocity, hits the ground at a rate which is equal to that attained by jumping off a wall which is 2 m high. (Call this rate v_{ground}.) Determine k/m. Hint: Calculate the velocity for a free fall from 2 m and equate it to the terminal velocity of the parachute.

• In order to avoid serious injury, suppose that the skydiver must hit the ground at a velocity that is within 5 percent of v_{ground}. By what altitude must the parachute be opened to satisfy this restriction? Discuss whether your answer is reasonable and how other restrictions might yield a different answer.