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3

It's very easy: projectile needs to trevel faster than speed of sound in media. That creates shockwave, wich is sort of explosion. For example, speed of sound in water is about 1,5 km/s. That means that even 10g bullet at that or higher speed could rip human limbs apart and kills even with seemly nonfatal body wounds. For soil and wood this speed is about ...

5

That's pretty straightforward. You know the mass of the bullet, you know the energy you want to deliver, and you know the relationship between the two through the velocity. Therefore you just need to put in the formula the energy and the mass and extract the velocity: $v=\sqrt{2E/m}$ A Mark 82 bomb delivers 227 kg of explosive. That corresponds to ...

7

Real-world example: Operation Plumbbob Cort's answer to this question is pretty great, but makes two faulty assumptions. One, the reentry vehicles aren't the fastest objects humans have ever made, and two, they're interacting largely with the top of the atmosphere. As evidenced by the host of other answers, the theoretical side of things is difficult at ...

3

The jet from a shaped charge is one of the fastest objects on earth: formed from a flat metal liner blasted into a narrow line by a conical explosive charge, it is still essentially solid (many erroneously describe it as a liquid), but at that speed it does not behave like one. Shaped charge jets are most effective when dense metals are used (eg tungsten) ...

4

For a given value of "projectile" and an arbitrary distance... Anatoli Bugorski was hit by a particle accelerator beam in the face. The accelerator in this case was the U-70, which can impart 76GeV on a proton beam. At those energies each proton would be travelling at close to 99.99% of the speed of light. You don't need to worry about the projectile ...

9

Just as food for thought: Some fraction of c (light speed). First, you fire a laser or something that will ionize the air between yourself and the target (= create a plasma). Think big: Something that ionizes a channel that is between 100 and 1 km wide. Bigger is better. Then you use electronic and magnetic fields to move as much plasma out of the way as ...

26

At what velocities would the (aerodynamically shaped) projectile just burn up? Only a few km/s. Read up on the Sprint missile, which could reach Mach 10 in 5 seconds (which would be about 3.5km/s, though that slightly depends on the altitude it had reached at that point) which resulted in skin temperatures of 3400 degrees C and needed an ablative heat ...

41

The answer depends on a mighty host of factors, including how pointy your projectile needs to be. However, we can put together a pretty reasonable upper bound by looking at reentry vehicles. They are pretty much the fastest manmade things in the atmosphere. Apollo 10 came in at roughly 11km/s. The record fastest reentry vehicle was Stardust, which came in ...

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