You’re driving on the highway, and a head-on collision is imminent. There is not enough time to swerve with any meaning. Would it be better for you and your passengers if you slammed on the brakes, or floored the accelerator?
Yes, this is a physics question, but feel free to address the morality of it.
Related bonus question: If you were trapped in an elevator in free-fall, would it do you any good to jump up with all your strength before the elevator landed (assuming you could time it just right)?
No. this is probably what the OP is thinking, but you are, along with the elevator accelerating downward at 32 ft/sec/sec, so you would not only have to time your jump perfectly, but you’d have to overcome your downward speed. Not happening.
As mentioned above, Mythbusters did a show on this, which was entertaining but came to the same answer as me. Everyone in the elevator is toast.
as for the other question, I’m at a loss. Accelerating straight on? Makes no sense. if he threw in a wiggle, like swerving while accelerating, maybe a different answer could be guessed. But speeding up would only make sure everyone reached their end state a little more quickly, most likely death, but not necessarily.
This part of his question makes no sense, perhaps he worded it incorrectly.
As to the elevator, the answer is that you can’t save yourself because you cannot jump hard enough to decelerate enough to make much difference, and you couldn’t time your jump as required anyway.
However, contrary to answers above, there is no theoretical physical reason why jumping would not work if you could jump hard enough and could time your jump correctly.
If (say) the elevator was falling at 30 m/s and you jumped hard enough to accelerate yourself to about 30 m/s upward relative to the elevator, and if you timed your jump such that as your feet left the floor of the elevator it hit the ground, you would experience no shock at all. At the moment of the elevator hitting the ground, your speed relative to the ground would be about zero. This isn’t quite right because your pushing against the elevator would speed it up a little, but it’s about correct, assuming the elevator is orders of magnitude more massive than you are. Timing is absolutely critical. Obviously a jump too late wouldn’t work, but equally if you jump too early (even slightly too early) you would hit the ceiling of the elevator at 30 m/s (relative to the ceiling), and the ceiling would then accelerate you downward till you were once more doing 30 m/s (going down) and then the elevator would hit the ground at 30 m/s. That is, you would double your problems.
No. See above. At the top of the fall, you have certain potential energy in the form of your height above ground level. As you (and the elevator) fall your potential energy is converted into kinetic energy (ie you are plummeting downward). When you jump you are shoving the elevator downward and you upward, transferring some of your kinetic energy to the elevator. You do not magically regain that energy in some way thereafter.
If it helps, think about this example: as above you and the elevator (which in this example has no ceiling and is open at the top, a kind of “convertible” elevator) are plummeting downward at 30 m/s having fallen from a height of about 50m. About 5m off the ground you jump hard enough to accelerate yourself to a speed of 30m relative to the elevator. The elevator plummets to the ground at a speed of a little over 30 m/s (due to you shoving it down with your feet). You are (momentarily) 5m off the ground, doing zero m/s relative to the ground. You then fall to the ground but now only (in effect) from 5m not 50m.
I’m not sure what you think the problem would be.
A slight difficulty would be getting into a position ready to jump since if you bent your knees they would (to some degree) just come up and your feet would leave the floor. However, there is still going to be some friction on the elevator from the walls etc of the elevator shaft so it would accelerate slower than you and so you could crouch ready for your jump. Or you could maybe grab a hand rail or something to lever yourself into a crouched position with your feet on the elevator floor.
Once you are in a crouch then jumping will accelerate the elevator down and you up.
That’s true for an elevator falling in a vacuum with no connection to any guiderails providing friction. In reality, there is aerodynamic drag on the flat bottom of the elevator and some friction/rolling resistance between the guide rails and the wheels/skids of the elevator, so the downward acceleration will necessarily be less than 32.2 fpss. Maybe not much less, but enough so that you could probably expect to maintain foot contact with the floor of the elevator and prep for a jump.
The utility of jumping is up for debate, and will obviously depend on just how fast the elevator is falling at the moment it hits bottom. According to this, a pretty good vertical jump is 40 inches, which corresponds to launch velocity of about 10 MPH. I would guess that a healthy adult could survive a drop of about twice that height without substantial risk of injury; 80 inches corresponds to an touchdown velocity of 13 MPH. So if the elevator hits shaft-bottom at 23 MPH, you could conceivably jump at the right moment to brake your own subsequent impact velocity to an injury-free 13 MPH (and then you’d immediately have to absorb that 13-MPH impact with your legs, which would feel like you had just jumped off of the top of a stepladder).
As elevator impact velocity increases, your last-minute leap still reduces your impact velocity by 10 MPH from whatever it would have been without jumping; your chance of injury goes up with elevator impact velocity, but your leap still reduces your chances and/or your severity of injury. At some point it doesn’t much matter; there’s probably not a lot of difference between hitting the floor of the elevator at 110 MPH and hitting it at 100 MPH.
Well, with the addition of the elevator question, I smell homework. And in that juvenile vein, I think what the OP is thinking is say if you’re in a big SUV and the car you’re about to hit is a compact would it be better (for you) to increase *your *speed to more ‘overpower’ the momentum of the smaller vehicle. To which the answer would be - No. All the (great many) other variables being equal the vehicle with the greater mass has an advantage, but adding more energy will just make things worse (for both).
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With the collision question the obvious answer is better it is better to break as the amount of energy in the crash varies with the square of the speed. The better question is would you rather die in a head-on collision or almost die in a head-on collision?
If your body could withstand the force of such a jump, then it wouldn’t be damaged by the force of the landing (if your muscles could time it right.) You’re absorbing the same amount of energy in either case.
Of course, the timing issue applies in either case (jumping just before the landing, or bracing for the landing as it happens.) In the latter case there’s the possibility of detecting and reacting to the landing, but not given human anatomy and nerve impluse speed, etc.
So let’s say you can jump to cancel out the speed of the elevator completely, you would hit the ceiling at close to the same speed. Assume an open elevator then wouldn’t you hit the floor of the elevator (now part of the ground) at the same speed the elevator hit it?
In fact, because the air in the elevator is at rest relative to the elevator itself, the difference in terminal velocity between a body and an elevator would not be relevant and from what I remember from physics*, wouldn’t you hit the ground at the same speed as the elevator no matter when and how high you jumped?
In particular, neglecting air resistance, the velocity you jumped up at equals the velocity you land with.
No. The whole point of jumping is to minimize your velocity relative to the earth at the moment that you restore contact with the floor of the elevator after jumping.
Example: Elevator is falling at 10 MPH. A fraction of a second before impact, you jump upward as hard as you can. As described upthread, you now find yourself moving upward at 10 MPH relative to the floor of the elevator - but at zero MPH relative to the earth. A fraction of a second later, the elevator hits the bottom of the shaft and comes to a dead stop. Since you are moving at about zero MPH, you now find yourself standing on the floor of the elevator, and all is well. Your head never need touch the ceiling of the elevator.
The only way you would contact the ceiling of the elevator is if:
A) you jumped way too early, or
B) the structure of the elevator is unable to prevent the ceiling from collapsing toward the floor when the floor impacts the bottom of the shaft.