Physics/Free falling question
Hi so I got into a debate with my friends about this, say I jump out off my floor which is 40 ft high and I have an object with handles equivelant to my weight 145( I am not sure if this matters but I think it does) and right before I hit the ground I jump off from this object would I die? It's only 40 ft so I think it would still be a significant difference In the velocity you're falling. Since Newton's law every action has an equal and opposite reaction I would slow my fall right?
Please forgive my delay in responding -- it's the only way I can think of, to ensure I am not assisting with academic work, of which homework is just a small part. Also, as I am unable to determine the veracity of what people post, I can not know whether or not a question involves academic work.
A fall of about thirteen meters (I've used metric units since I was in high school) is near the median height of fatality for a fall
but there are so many variables that it is difficult to make an exact determination of how much difference this is going to make. Sadly, I found it pretty much impossible to get an answer to the question: what is the mortality rate for falls from specific heights? So we'll just say that a fall from that height is in the category of, "Viewers, do not attempt this at home!"
For a fall from this height of any object over a few kilograms, you can pretty much ignore air resistance. Also, the exact mass of the falling object does not matter, as shown by John Philoponus.
That means you'll be falling about 1.6 seconds (that answer will be left as an exercise for the reader), and you'll hit the ground with a velocity just over fifteen meters per second. The question I presume you're asking is whether you can reduce YOUR velocity by making another object go faster downward, to an extent that your survival rate goes up significantly.
Ignoring the fact that this would take incredibly precise timing, we can ask whether or not we humans can generate enough force to give ourselves enough upward velocity to significantly negate the fifteen meter per second downward velocity. In other words, what is the maximum upward velocity we can generate with our muscles? Let's make a general estimate.
Again, if we neglect air resistance, an object with initial upward velocity of V on our Earth's surface will lose velocity (ie, decelerate) at a rate of 9.8 meters per second squared. If we're traveling downward at fifteen m/sec, we would need to exert enough force on the other object to go upwards at eight m/sec; any less and it wouldn't make enough difference to avoid serious injury. Again, whether this means you'll survive is impossible to determine.
If we could generate that type of upward velocity while standing on the surface of our Earth, we would reach our maximum height when our total velocity became zero -- ie, when
V = a(g)t
where a(g) is the acceleration of gravity and 't' is the time.
At this point, the distance traveled 'd' is given by
d = v(average) t
Again, the above will be left as an exercise for the reader.
Being able to give ourselves an upward velocity of eight m/sec would be the same as being able to leap three meters in the air from a standing high jump WITHOUT bending our knees or moving our legs after leaving the ground.
So, it cannot be done. Even lifting your feet just one meter off the ground, from a standing start and without knee bending or leg movement, would be difficult.
This is similar to the "how to survive an elevator fall" myth that's been repeatedly debunked: