Can't explain to my friend properly

[Fred]

Hi
My first post so be gentle
My friend asked me these two questions and i can explain them to myself but i can't explain them to him very well.

These are as he put them.

1. If a lorry is traveling at 60mph and has a ramp on the back so that a car can drive up the ramp into the back of the lorry the car must travel faster than 60mph to get on to the ramp. So when the car gets on to the ramp it is still going at more than 60mph so how can it stop before it hits the front of the lorry as the braking distance is quite big and certainly bigger than the length of the lorry. (like in the italian job)??

2. in cartoons when an aeroplane is dropping in free fall and the cartoon man steps out of the aeroplane 2 feet off the ground and so survives the crash. Would this work in the real world??

hope someone can help
thanks
Fred

 

[russ_watters]

1. A lorry is a truck, right? If the car is only moving 1mph (for example) relative to the truck, it doesn't have to slow down very much, does it? But, the wheels are still spinning, so you'll get a little jolt and leave some rubber on the ramp (as an airplane does when it lands).

2. No - the man is falling at whatever speed the airplane was falling.

3. Welcome aboard.

 

[Gonzolo]

From a 100% mechanics point of view, I think it would be possible for something to pop out upwards out of the plane at 2 feet above the ground and be safe. It would have to have enough power to speed upwards at minus the planes falling speed, pretty much exactly. Debris, fire, the lack of a good jumping surface, and weekness of a man's legs in reality maintains the cartoon at fiction level.

 

[VantagePoint72]

Just in case that's not clear enough...
As russ said, if the lorry's traveling at 60mph and you're traveling at say 65mph then when you get onto the truck your speed is really only 5mph...however, you're wheels have been spinning fast enough for you to be doing 65 on the ground. So while you don't hit the ramp at a high speed, you're wheels are still spinning extremely fast. So, like russ explained you'll jump forward about when your wheels catch on the ramp, however since your initial speed relative to the lorry was low enough you'll still have plenty of time to stop. So if you (or your friend) can imagine your wheels spinning really fast but uselessly as you slide at only say 10mph on a patch of ice and then catching on the pavement after the ice as you slam on the breaks, you can see that won't have enough speed to require a breaking distance longer than available. And yes, in both cases you will leave a nice trail of rubber.

I agree with the no. If you're traveling toward the ground at 100mph (that's a completely random number but imagine quite low for a free-falling airplane), and then you jump up off the plane at around 3mph it's not going to do a whole lot to the speed you hit the ground with. And even if you could somehow leap upwards at 100mph, such fast acceleration upward (or negative acceleration upwards against your original speed) would be sufficient crush you like a bug. I imagine it's still a much better idea to bail out when the plane starts falling.

 

[Gonzolo]

I agree with the no. If you're traveling toward the ground at 100mph (that's a completely random number but imagine quite low for a free-falling airplane), and then you jump up off the plane at around 3mph it's not going to do a whole lot to the speed you hit the ground with. And even if you could somehow leap upwards at 100mph, such fast acceleration upward (or negative acceleration upwards against your original speed) would be sufficient crush you like a bug. I imagine it's still a much better idea to bail out when the plane starts falling.

I think air friction limits freefalling speed to some either 180 mph or 180 km/h (in the hundreds anyway), so the number is not so far off. I agree the upwards acceleration of a free body would be of the same order of magnitude as the crash itself. A jetback would be needed to control it. For what it's worth, Guiness world records cites that a woman was found alive once in a plane that crashed from 35 thousand feet above Russia. While the record for a surviving freefalling human is a few thousand feet I think, much less anyway.

 

[Fred]

Thanks a lot everyone that's exactly what i thought but it was getttin git into layman terms that was hard. The second one is like the whole thing with jumping at the right moment in a plumeting elevator now that i think about it so i can use that one to help him understand.

Thanks again
Fred

 

[kuengb]

From a 100% mechanics point of view, I think it would be possible for something to pop out upwards out of the plane at 2 feet above the ground and be safe. It would have to have enough power to speed upwards at minus the planes falling speed, pretty much exactly. Debris, fire, the lack of a good jumping surface, and weekness of a man's legs in reality maintains the cartoon at fiction level.

The falling-elevator-thread is back again...

 

[Doctordick]

A simple comment!

I have noticed that no one has made any specific calculations on the problem of jumping to avoid death. I would have expected more on a physics forum. A rough estimate of the circumstance is quite easy.

The best high jumper in the world jumps somewhere around eight feet. Now he actually only raises his center of gravity about four feet (I use round numbers to make things easy). His velocity when he loses contact with the ground is given by v\,=\,\sqrt{2gh}. (Note the convenient numbers I have chosen) his maximum vertical velocity is the square root of 2*32*4 which is exactly 16 ft/sec. That translates to 10.9 miles per hour.

It follows that, with perfect timing (i.e., he hits the ground the moment his feet leave the surface he is jumping from), he could remove 10.9 miles per hour from that terminal velocity of the elevator (what, something between 100 to 150 miles per hour). It should be pretty obvious that jumping is pretty well a waste of time.

Have fun -- Dick

 

[VantagePoint72]

Fred never asked for numbers, Dick. Just how one thing is possible and if something else is possible. No need to expect more on a physics forum that has the word help in it's title- sometimes people prefer an answer without math.

 

[PFanalog57]

It follows that, with perfect timing (i.e., he hits the ground the moment his feet leave the surface he is jumping from), he could remove 10.9 miles per hour from that terminal velocity of the elevator (what, something between 100 to 150 miles per hour). It should be pretty obvious that jumping is pretty well a waste of time.

Have fun -- Dick

When the jumper hits the ground there will be a rapid change in momentum for a very short period of ...time

Impulse = Change in momentum

The magnitude of the momentum change will be proportional to the force and the length of time that the force acts.

The kinetic energy of the fall will be equal to the potential energy:

mgh = mv^2 / 2

g is acceleration due to gravity and h is height from the ground.


If the jumper lands on a surface of pure marshmallow, then the time of the momentum change will be much longer. Deceleration will be less. A hard surface at impact would mean an abrupt stop and the force would be much greater than mg?

F = mDv/Dt

The larger Dt[change in time] , the less the impact force.

Of course, water is not a hard surface, but it can be, from falling.

Belly flop at terminal velocity of 150 mph?

ouch!

 

[Gokul43201]

Also - if the jumper's legs have the strength to accelerate him to ~100 mph then they should have the strength to absorb a landing at the speed of 100 mph.

 

[Gonzolo]

Yup, but at least he would avoid the flaming wreckage. It might be an option for a black box. We know it can stand the upwards acceleration of a crash, so it could instead be shot out of a cannon (and perhaps fall in a parachute), providing the extra security of being away from the chaos of the wreckage.

 

[Gokul43201]

Yup, but at least he would avoid the flaming wreckage.

True...so jump horizontally !

 

[Gonzolo]

There could be a tree.

 

[colinr]

I didn't realize trees could grow out of marshmallow, or wait a mintue this is a cartoon so i guess its okay

 

[Gonzolo]

There could be a fork!

 

[Artman]

...The second one is like the whole thing with jumping at the right moment in a plumeting elevator now that i think about it so i can use that one to help him understand.

Thanks again
Fred

Actually, your pushing off the elevator floor acts in both your motion and that of the elevator. The average elevator has more mass and therefore more inertia than the average person, so you would move more as a result, but your pushing would add to the speed of the elevator's downward motion, taking away some from your possible upward motion. So when you jump you push down the elevator some and push you up some.

 

[Kelju Ivan]

Regarding the first question: The way I see it, when the car gets on the lorry it's no longer moving on the same surface (can't find the word I'm thinking of). At first they're both on the road with speeds of, let's say, 60 and 65mph. Now when the smaller car is on the lorry, it would move at 60mph even if it didn't use its own engine at all. Doesn't this mean that it would move at 65mph relative to the lorry it's driving on, thus making it very difficult to stop before the end of the ramp?

...I gave some extra thought to the answer given earlier. The braking is started when the front wheels touch the ramp. This would make the speed difference less, but when the back of the car is on the truck it would still have a much larger relative speed. What am I missing here?