When you fall on Earth, gravity pulls you towards the ground while air resistance slows you down. The air resistance increases as you go faster, so after a while, you reach “terminal velocity” and stop experiencing significant acceleration.

When you
change your velocity, you experience acceleration. There are a number of
relationships between position, velocity, and constant acceleration, but the
one that is relevant here is:

You will be
falling at terminal velocity for most of your fall and will only change your
velocity significantly when touching the trampoline. If the trampoline stops
you or you hit the ground, your velocity will be zero. If the acceleration is
too high, you will be injured and/or die.

The best
case scenario then is that the trampoline exerts a constant acceleration on
you. If it were not constant, then at some point the acceleration would have to
be higher than in the constant case which is worse for you than if it were
constant. Thus, we can assume that the equation above applies here.

The distance
traveled in the equation is the total distance traveled while touching the trampoline
and the change in velocity is the terminal velocity since terminal velocity
minus zero is equal to terminal velocity.

We just need
the numbers to plug into the equation. Terminal velocity varies, but 55 m/s (125
mph) is a reasonable value to use. Trampolines vary in height, but 1 m (3 feet)
is a reasonable height for one. Plugging those values in, you get:

What does this value
mean? One “g” is the acceleration we feel on the surface of the Earth and is
approximately 10 m/s^2, so this is approximately 150 g’s. 100 g’s is often considered
the maximum acceleration that a human can handle, so unfortunately, while the
trampoline probably won’t hurt, it probably won’t help much either.

#### Random Thing

Professor
Splash was a contestant on America’s Got Talent whose talent was to dive from
seemingly impossible heights into a shallow pool of water and survive. How was
this possible?

One of his
most impressive dives was 36 feet 7 inches (add meters here). Ignoring air
resistance (worst case scenario for Professor Splash), his speed was
approximately 33 mph (~15 m/s) when hitting the water. Since the water was ~1
feet (~0.3 m) deep, if we assume a constant acceleration, we get the following
using equation n:

Again, using the 1 g = 10 m/s^2 conversion, we find that
he experienced ~37.5 g’s. This is enough to be quite painful and potentially
cause serious injury, but it is definitely survivable for short durations (e.g., major hits in American football create higher accelerations).

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