QUESTION #54

# If I were in an elevator that was free falling, would it help at all if I perfectly timed a jump before it hit the ground floor? Would anything help the situation?

In a state of free fall, both you and the elevator are weightless, and jointly approaching the bottom of the shaft at the same high velocity. You are in a similar position to an astronaut floating around in his capsule or spaceship, unable to stand or get a secure footing on anything without recourse to magnetic boots and/or ropes and handles to pull against.

Therefore, so far as jumping is concerned, it may be possible to make some very rough inefectual attempt, but remember in a state of free fall, you do not have the huge mass of the Earth to steady you and push against only, by comparison, the minute mass of the elevator car. You may in your weightless struggles succeed in pushing yourself away from the floor of the elevator and bumping on the roof but your original velocity will be little, if at all, diminished, certainly not enough to save you, and impact with the roof of the elevator will restore your velocity. Remember also that astronaut has days, months, to push and pull himself around, you in the elevator have only seconds.

Disregarding any resistance due to friction or air pressure which would destroy the concept of free fall, after little more than 4 seconds your velocity is about 40 metres per second or say in the region of 90 miles per hour and increasing every instant. If you are say a person weighing 80 kilograms then your momentum P=MV, that is P = (80Kg) times ( velocity 40 metres per second) ie 3200 kilogram meters per sec. This increases every instant because of the accelleration due to Gravity which is 9.8 meters per second every second. Your problem is somehow to get rid of this building momentum before you do so at the bottom of the shaft. You certainly cannot reduce your mass of 80 Kg.The human body is not capable, even under normal circumstances of jumping upwards at 40 meters per second or 90 miles per hour if you have it in mind to reduce your velocity to zero by moving at a similar speed in the opposite direction. As indicated above jumping in the conventional sense of the word is not possible. A sudden jump a split second before you and the elevator impact the ground, were this posible, would be no good, for you would similarly crush yourself by the abrupt onset of the required force in the opposite direction, which is similar to what happens if you hit the bottom of the shaft.

What you need is space, in which you can gradually reduce your velocity, and an elevator which has no roof. Retro rockets strapped to you waist could work provided their counterthrust in the opposite direction to your fall did not have too rapid an onset.. Your downward plunge would be gradually arrested whilst the lift fell away from you , Similarly a parachute, if it could be made to deploy and work within the confines of the lift shaft could save you, but remember things are happening very quickly and time and adequate space for arresting devices are not on your side.

In point of fact being in the elevator is practically irrelevant, for the position is almost exactly the same as if you had jumped into the shaft, you can readily imagine the hoplessness of the situation and the maximum distance you could fall and survive, a few meters perhaps. Thus lifts in free fall and at high velocity are to be avoided, as death is almost certain.
Answered by: Don Bird, Berkshire UK