if I go sky diving from 13,000 how fast and how long will I be in the air?

Question

also could you provide the equation? I have been trying to figure it out and am getting different answers each time! thanks!!!!

Answer 1

First, find the time needed to travel -32000 ft with an acceleration of -32 ft/s^2.

d = 1/2 at^2
t = sqrt[2d / a]
t = sqrt[ 2 * -13000 ft / (-32 ft/s^2) ] = 28.5 sec.

And now find the maximum velocity (the velocity at the moment just before you hit the ground).

v =at
v = (-32 ft/s^2)(28.5 s) = -912 ft/s

That's equal to 622 mph, but this is not realistic because we're not taking air resistance into consideration. One can find what the time and speed would be with air resistance, but it's rather time-consuming to do so.

From wikipedia, the force due to air resistance is F = 1/2 pv^2 Ac where p is the density of the air, v is velocity, A is cross-sectional area, and c is the drag coefficient.

The force due to gravity is F = ma = -mg, so the total force at any given time would be:
F = 1/2 pv^2 Ac - mg
ma = 1/2 pv^2 Ac - mg

The differential equation you would solve to get v(t) is:
m dv/dt = 1/2 pv^2 Ac - mg
v(0) = 0

Then, you would have to integrate v(t) and use d(0) = 35000 to find d(t). Then, after doing all of this, you could set d equal to 0 and find t, and then plug that value of t back into your expression for v to find the max speed.

But this wouldn't even be right! If you look at the wiki link on terminal velocity, you can see that you have not two, but three variables when you recognize that the barometric pressure also changes as you fall:

"Note that the density increases with decreasing altitude, ca. 1% per 80 m (see barometric formula)."

I haven't taken a multivariable calculus class yet, so I don't even know how you would go about solving this kind of problem with three variables.

Answer 2

Sky dive. As uncomfortable and embarrasing because it might want to be, the deep see diving in a gown might want to eaisly be deadly. That a lot fabric around the legs and entering into kit might want to correctly drown you.

Answer 3

It depends in some sense on your mass and the speed at which you eject yourself from the plane. Assuming you were simply dropped from a standstill at that height, your acceleration would be approximately 9.8 meters per second squared,

One common unit of acceleration is g, one g (more specifically, gn or g 0) being the standard acceleration of free fall or 9.80665 m/s², roughly caused by the gravity of Earth at sea level at about 45.5° latitude.

but this would increase exponentially based on your mass and the distance you fell - based on the Newtonian principle of v=m*a. The rate of acceleration might be a little bit different at 13k feet, since that calculation is based on gravity at sea level. Take your weight and multiply times the acceleration factor, and you can calculate both your velocity and the number of seconds it would take to reach impact. Also, you'd need to account for reaching terminal velocity:

The terminal velocity of an object falling towards the ground, in non-vacuum, is the speed at which the gravitational force pulling it downwards is equal and opposite to the atmospheric drag (also called air resistance) pushing it upwards. At this speed, the object ceases to accelerate downwards and falls at constant speed. An object moving downwards without power at greater than the terminal velocity (for example because it previously used power to descend, it fell from a thinner part of the atmosphere or it changed shape) will slow down until it reaches terminal velocity.

For example, the terminal velocity of a skydiver in a normal free-fall position with a closed parachute is about 195 km/h (120 Mph). It would take about 5.5 seconds to reach that speed. This speed increases to about 320 km/h (200 Mph) if the skydiver pulls in his limbs—see also freeflying. This is also the terminal velocity of the Peregrine Falcon diving down on its prey.

So, you'd reach 195km/h after 5.5 seconds (or 320 if you tuck in your arms and legs) and then fall at a constant rate for the rest of the distance until you hit. You will need to convert 13000 feet into kilometers, but rough order of magnitude is about 2.5 miles or 5.5 km of falling distance at either rate of speed. I'm figuring 5280 feet in a mile and 2.2 km per mile.

By my calculations, 195 km/h is 3.25 km/s, and 320 km/h is 5.3 km/s, which is pretty damn fast. It would not take more than a couple of seconds for you to hit the ground upon falling from that distance, unless of course you had something to induce drag, like a parachute.

Answer 4

Try it and see.