Easy Month: Jumping in the Lift

Bengt is watching "QI" on BBC. It's the kind of show which really gets Bengt going, because he doesn't want to accept that people know things he doesn't.
The show brings up the old myth of the falling lift - that if you are in a lift, and the cable snaps so that the lift falls, you can save yourself by jumping just before the lift hits the ground. Since you are not standing on the lift floor when it hits the ground, you would supposedly be unaffected by the impact. Bengt doesn't believe in the myth, of course, and has nothing but contempt for anyone who does. But still, it gets him thinking.

By jumping just before impact, you would after all get a certain speed upward, to be added to the speed downward which you already have. How high can a person jump? Bengt looks for the world record for standing high jump; his sources claim that it is 1.914 m. This, incidentally, very closely matches the height of Stephen Fry, the host of the show. Bengt pictures one Stephen Fry jumping over another Stephen Fry, and finds the image very amusing. Now, that record isn't for the center of mass, and we can't expect an average lift jumper to match the world record anyway, so Bengt decides a person can jump 1 m, for physics purposes.

How high would the lift fall? Not every lift goes up hundreds of meters, Bengt reasons. Suppose you fall 4 storeys. How high is a storey? Well, Bengt thinks, it should be high enough that Stephen Fry wouldn't bump his head if he jumped, so that makes 2.914 m. (Bengt is forgetting that floors aren't infinitely thin, but it doesn't matter.) In the lift, hitting your head on the ceiling shouldn't be a problem, if you jump at the right moment.

Bengt realises that this problem would be tricky to solve without a calculator, and therefore gives you the extra clue that (2*√(2.914)-1)^2 / 2 = 2.914.

1. The impact after jumping would be equivalent to falling from a slightly lower height. How many storeys might that be?
2. The show claims that the best thing to do is to lie down on a fat person to cushion your fall. Why might it be tricky to lie down in a falling lift?
3. A lot of people are afraid of lifts, partly because they think that the cable might snap and the lift fall down. In fact, this is extremely unlikely. In the year 2000, modern lifts had been around for about 150 years, and there were 6 milliard people in the world. According to Bengt's mysterious sources, there was one lift per 1000 people, and the average lift made 200 transportations of people per day. By assuming that the lifts were built at constant speed - the number increased linearly from 1850 to 2000 - Bengt is able to calculate the risk of such an accident happening to a given person on a given lift ride; it is 0.000000000003%, making the modern cable lift probably the safest vehicle ever invented.
   How many times had such an accident happened?