This question is actually composed of two separate questions.

First part

First, let us assume that a heavy object of mass $m$ collides into me while moving at velocity $v$, and I'm standing still.

I assume this would hurt, but my first question is what affects my chances of getting hurt? Is that the initial impulse ($p=mv$) of the object, or is it the force ($F\approx mv/\Delta t$) exerted on me during the collision? Assuming the force is the relevant quantity (or else their would be no point in airbags), what is the maximal force allowed to avoid injury?

Second part

Now let us assume that the same object collides into me while we are submerged underwater. Furthermore, the object possesses the same momentum ($p=mv$) prior to the collision. Would the consequences be the same? more severe? less severe?

My dilemma regards the medium. Since water are incompressible, I should start "feeling" the body "pushing" water towards me earlier, thus the effective duration of the collision is longer, which should imply smaller forces. On the other hand, the "wet" weight is larger than "dry" weight, thus I experience more impulse, especially if for instance the hitting body has some cavity which may be filled with water thus giving it larger effective mass during collision.

Aside from that, since the collision in water cannot be thought of as sudden, how should I acount for drag forces during the process?

I know this is long and complex, but I'd love to hear your thoughts on the matter.

  • $\begingroup$ No offence, but I think you need to read the physics definitions listed here: en.wikipedia.org/wiki/Impulse_(physics) $\endgroup$ – user198207 Jul 17 '18 at 20:22
  • $\begingroup$ I'm well aware of impulse. However, what does the article have to do with collision of submerged bodies? $\endgroup$ – Yair M Jul 18 '18 at 5:58

The first part. I believe it is the impact force per unit area (pressure). The maximum impact force without causing injury would depend on the part(s) of the body impacted. It's a bio mechanical engineer problem.

The second part. Wow, not sure. But for a given kinetic energy of the object at the moment of collision, I would expect the water would make things worse because it will exert a force resisting motion of the person's body. Compare the effects of you standing against a brick wall vs nothing behind you.

  • $\begingroup$ +1 for pressure, but there are many other factors with water. It can "absorb" or "redistribute" energy/forces... $\endgroup$ – selya Jul 17 '18 at 22:16

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