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If a typical human were shrunk down to be 3cm tall weighing 2.5 grams (ignoring all problems that would cause), would the blade of the grasslike plant described below be able to stop its fall from 6 inches up?

The grass has a rough texture as shown below

grass texture (image source)

The blade of grass is at a 70 degree angle and measures 2 ft long and 1 ft wide curling in on the sides (so he doesn't slide off) and comes to a point on the end. He lands half way down.

Would it be possible for him to come to a complete stop before touching the ground?

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  • $\begingroup$ What is the mass of the shrunk human? $\endgroup$
    – sphennings
    Commented May 9, 2017 at 23:30
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    $\begingroup$ You could probably drop a ~0.4g (that's (3cm / average male height)³ x average male weight, very back of the napkin style math) object onto large houseplant leaf to get a guess. $\endgroup$
    – Jason C
    Commented May 9, 2017 at 23:33
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    $\begingroup$ That could work, too. In general for scale models of 3D stuff the mass is (scale^3)*weight but I'm sure you can take some creative liberties with his weight, 2.5g seems totally imaginable, too. So drop a half a crayon on a plant. Btw, like the crayon, unless he was very agile, he runs a pretty significant risk of bouncing off or sliding off on the way down. But I suppose it's not uncommon to have people in fiction pull off some pretty physically amazing stunts. $\endgroup$
    – Jason C
    Commented May 9, 2017 at 23:37
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    $\begingroup$ @JasonC Congratulations on proposing an experimental method to answer the question. The scaling should be by volume, assuming constant density, although the cube rule based on height is a good approximation, so your formula gives a very usable answer. Keep up the good work. $\endgroup$
    – a4android
    Commented May 10, 2017 at 1:38
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    $\begingroup$ @Kilisi he's unconscious. $\endgroup$
    – Cameron Leary
    Commented May 10, 2017 at 14:21

2 Answers 2

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Take a hundred foot mine shaft, drop mouse down it and the mouse will land uninjured. A person sufferong a similar drop will break every bone in his body. An elephant will splash.

The smaller an animal gets the less a fall can hurt it. Terminal velocity for small things is just too slow. Assuming the humans muscles don't shatter his miniscule bones during normal movement a fall is not going to bother him at all, so he doesn't need the grass. Buts lets say he wants to use it anyway.

Grass is a pretty wide description as well, some grasses would stop him no problem other would not, just make it wider and more rigid if you don't think it will work. Something like zebra grass would work no problem.

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  • $\begingroup$ Small edit to make it more clear. $\endgroup$
    – John
    Commented May 10, 2017 at 0:42
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No

70 degrees is a really steep angle. If your tiny man was conscious, there's a chance he could grab onto some protrusions and slow himself down. Unconscious, though, there's simply not enough to keep him on the leaf.

After 6 inches, he'll be moving at about 1.73 m/s. I second @JasonC's experimental suggestion just to make sure, but that's fast enough I would expect him to hit the leaf, begin sliding down as the leaf bends under his weight, then the leaf springs back and throws him off.

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