Would you survive if you were hit by a grain of sand traveling 99% the speed of light?
a interesting post i found by: Janko Jerinic
Let's compare the kinetic energy that the grain of sand would have to something we could relate to a bit more easily. As we know, kinetic energy of an object is proportionate to the mass of the object and the square of its velocity.
Velocity of the grain of sand is close to 3e8 m/s. Let's compare that to the velocity of a free-falling object, near Earth. There, acceleration of free-falling objects is approximately constant and roughly equal to 9.81 m/s^2, but let's round it to 10 m/s^2. Therefore, object reaches 30 m/s in Earth's gravitational field, after just 3 seconds, covering approximately 45 meters. That's a little over 100 km/h, for you car-lovers, but exatly 1e7, or ten million times less than the velocity of the grain of sand.
Remember that - I am dropping an object from the height of 45 meters (about 15 building floors) and it hits the ground after 3 seconds, speeding at over 100 km/h.
Okay, back to kinetic energy. Our falling object flies at 30 m/s and the grain of sand at almost 300000 km/s, which is 10 million times faster. I want to know what kind of mass I need to hurl so that its kinetic energy would be equvalent to that of our super-fast grain of sand. Since we established that kinetic energy is proportionate to the square of the velocity, and the velocity of the object is 10 million times less than that of the grain, our object needs to be 100,000 billion (1e14) times more massive! Your average grain of sand has the mass of around 1e-9 kg, so our object of equal kinetic energy would have to have the mass of around 1e5 kg, or 100 tons!
So, let's sum it up:
A 100-ton object, falling from 45 meters, reaches the speed of over 100 kmph as it hits the ground, 3 seconds after it has been released. This object has roughly the same kinetic energy as the grain of sand, travelling nearly at the speed of light. (I've rounded off your 99% as it doesn't make a significant difference, and I've rounded our planet's near-surface gravitational acceleration)
Imagine getting hit by 100 tons of something travelling at 100 kmph? Some kinetic energy, huh? However, we haven't taken into account the super-small dimensions of the grain! This is relevant because, if your body were to absorb all that kinetic energy, you would be seriously in trouble. Luckily, your body isn't a rigid object and collisions with the human body are not perfectly elastic. If it were, then force induced by a collision across any contact area would be distributed over your entire body and that little grain of sand would send you flying. Due to its very high energy and small dimensions, your body would be relatively transparent to the grain, kind of like how materials are transparent to EM waves of small-enough wavelengths. So, when a super high-energy grain of sand hits our skin, it immediately breaks all cell bonds orthogonal to its penetration direction. This disconnect stops the distribution of collision force across the surface of the body and the rest of your body almost doesn't feel the impact. The grain pushes on forward on its path dissipating a little bit of its energy on friction, raising local temperature.
Therefore, a grain would puncture a near-perfect little hole through your body, but you would most likely survive, because such a tiny object couldn't rip apart enough tissue area of any vital organ. One might argue that the wounds would be cauterised on the spot.