# Can a Skydiver Land On a Large Slide and Survive?

You try to differ between impact and sliding on a curve. In fact the impact is just a sudden large force, while a curved (e.i. circular) motion similarly applies a force, just much smaller but also over a longer period of time.

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The key in surviving any fall is to reduce the force on your body at "impact". A pillow does that. A curved slide does that. And they both do it by extending the impact duration. Remember first Newton's 2nd law:

$$\sum\vec F=\frac{d\vec p}{dt}\approx \frac{\Delta\vec p}{\Delta t}$$

Smaller momentum change $$\Delta \vec p$$ (that would be smaller speed or lighter skydiver) or larger duration $$\Delta t$$ will reduce the total force. A soft material like a mattress will extend $$\Delta t$$. And a curved slide will as well, as you explain it yourself, cause the momentum change over a much longer period of time.

Let's make life easy for ourselves by assuming that the slide is an arc of a circle:

We also assume the slide is made out of something with a very low friction, so the skydiver maintains a constant speed $v$ all the way round. The reason that using an arc of a circle makes life easy is that the acceleration felt by the skydiver is simply:

$$a = \frac{v^2}{r}$$

where $r$ is the radius of the circle (the length of the dotted lines in the diagram). The acceleration is shown by the red arrow, and always points towards the centre of the circle.

Let's take the terminal velocity of the skydiver to be 50 m/s, and let's suppose they can survive an acceleration of 10$g$ (98.1 m/s$^2$). If we rearrange the equation to get:

$$r = \frac{v^2}{a}$$

then to achieve this the slide would have to have a radius of 25m, which is actually quite reasonable.

In practice there would be a few problems of course. You'd have to land in exactly the right place at the top of the slide, and after you'd left the slide you'd still be travelling at 50 m/s but horizontally rather than vertically.

I have slid down a much smaller version of this at Burning Man. Paha'oha'o was a 30 foot tall volcano art piece which you climbed and then "sacrificed" yourself by dropping into a pit featuring a slide just like you mention. The drop features a 10 foot free-fall, just enough to take your breath away, after which the careful curve of the slide gently catches you and spits you out horizontally... rather fast. Safety Third!

It is much more intimidating at night, all lit up red and you can't see what you're dropping into.