Sunday, April 10, 2016

Published April 10, 2016 by with 2 comments

Can A Trampoline Save You If Your Parachute Fails?

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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