OK, here’s a question that I probably learned the answer to back in JHS physics. And, I’m sure the answer is on the board here in any number of threads. But when I searched I couldn’t find it, and there was just too much to sift through anyway.
OK, here it is:
When falling to earth, does your speed ever max out or do you keep accelerating?
The question came up in a conversation about skydiving I had last night. I took the side that you continue to accelerate as you approach the earth because the gravitational pull is stronger the closer you get. Thus you are always travelling faster at t + 1 than you are at t.
But the opposition (everyone else) claimed that your speed does eventually level off and remain constant the rest of the way. Someone brought up the point that if acceleration did continue to increase indefinitely you would eventually reach the speed of light (assuming no restrictions on the distance from earth at which you began falling) which is, of course, not possible.
I must admit, I just don’t know. It seems like something I should know, but I’m feeling quite dumb at the moment (soon to feel dumber?).
Gravity changes with distance to the center of the earth are not applicable at skydiving altitudes. Terminal velocity is reached when force from air resistance is equal to the force of gravity on the falling body’s mass, AKA its weight. Note that terminal velovity will increase with altitude because the thinner atmosphere provides less resistance while weight is virtually unchanged.
What with friction and air densities and all, I’d wager the increasing drag due to air density overcomes the increasing gravitational pull due to decreasing distance from the earth.
Terminal velocity in the situation you mentioned is regulated by wind resistance, so your terminal velocity would be much different from an ant’s.
So everything falling to earth has a terminal velocity, but in theory you could keep falling toward something in space and accelerate to the speed of light, me thinks.
Actually not even in space. Falling from a great distance to a gravitational body just accelerates you to the escape velocity of the body to which you are falling.
Don’t know what you look like, so I can’t say for certain, but probably yes.
Your terminal velocity would be higher than in an atmosphere, but not infinite. Falling from infinity through a vacuum will bring you to “escape velocity”. The escape velocity of the earth is that speed with which you must throw an object if it is to escape. (Rising objects decelerate at the same rate as falling objects accelerate.)
Okay. Bear in mind that escape velocity depends on your distance from the object as well as the object’s mass. At every altitude, escape velocity is equal to the velocity that you would have acquired by falling from infinity to that altitude. So if you fell from infinity and reached the escape velocity of Earth’s surface (Mach 24, if memory serves me), the reason that you would stop accelerating at that point is that you would have hit the ground. If you were lucky enough to fall down a deep mineshaft (and neglecting wind resistance) you would continue to accelerate: The escape velocity of Earth is higher below the surface, and it falls off with altitude.
What definition of luck are you using? You’d hit harder and take longer to do it! Not to mention the fact that your chute didn’t open in the first place.
Assuming the simplest model for air resistance (no fluke updrafts, or anything like that), your speed will level off, and it’ll always be increasing. Your speed will asymptotically approach terminal speed, always getting closer and closer, but never quite reaching or passing terminal speed. It’s a smooth, gradual transition.
