# Q & A: Opening Parachute

Q:
If a parachutist jumps from a plane and ends up moving at a terminal velocity the resultant force acting on him when moving at terminal velocity is 0 correct? That means that the air resistane force is equal to the gravitational pull of the earth (not cosidering other forces). When he opens the parachute air resistance icreases so the body deccelerates. Now my question is : As air resistance increases and the gravitational pull of the earth on the man (mg) is constant this means (according to Newton) that the resultant force is upwards and that doesn`t change. If this is true then at a certain moment the body will start to move upwards and as we know this is impossible. Now is Newton wrong or am I confused. Thanks for reading my question.
- Ylli Bole Kopani (age 17)
Vlora
A:
Ylli- You're right up to a point. The resultant (that is, the total) force on the parachutist's body right after the parachute opens is upwards. According to Newton's third law, the parachutist will accelerate in the upwards direction. This does not mean he will move in the upwards direction. The parachutist is moving rapidly downwards before he opens the parachute, and acceleration upwards really is the same thing as deceleration downwards -- he just slows down.

If the upwards acceleration continues unchanged for a long time, the parachutist eventually will start moving upwards. This doesn't happen in the case of the parachute, because force due to air friction changes strength (although it still points up). The strength of the air friction force depends on how rapidly the parachute is moving through the air. As the parachute slows down, the upward air friction force drops. It gradually gets very close to equal to the downward gravitational force, leaving almost no net force and thus a new terminal velocity, which is now less than the one with the parachute closed. So although the acceleration is upwards, it never leads to an upward velocity, but just slows the downward velocity to a new, smaller value.

There's a key math idea behind this, and perhaps confusion about it led to the confusion about the physics. You can add an infinite number of positive numbers (say little upward changes in velocity) and still never exceed some limit (say the initial downward velocity.) Think of adding the numbers 1/2+1/4+1/8+1/16........ It's not hard to see that no matter how far you go, you never get bigger than 1.

Mike W.

(published on 10/22/2007)