What is the maximum speed of gravity on a falling object?

Typically we consider the terminal velocity of an adult person free falling through Earth's atmosphere to be around 120 mph, more or less. The exact velocity depends on a number of body specific characteristics. It also depends on the air density the body is falling through.

Terminal velocity is the velocity at which the falling body ceases to accelerate while falling. Thus, f = ma = 0; the net force on the falling body is zero at terminatl velocity V and no longer falling faster.

Therefore f = W - D = mg - 1/2 rho Cd A V^2 = ma = 0; where W is the weight of the falling body (e.g., the baby) and D is the drag friction force that acts against the pull of gravity we call weight. rho is air density, Cd is the coefficient of drag, A the cross sectional area of the body, and V (when a = 0) is the terminal velocity.

We can solve for V^2 = W/(1/2 rho Cd A). From this, it is clear that V can be varied by the weight of the body, the density of air, the coefficient drag, and the cross sectional area. Perhaps those babies were very light, but had relatively large cross sectional areas (A) or high drag coefficients from the way they were shaped. In which case, it is feasible, if not likely, that the baby terminal velocities were less than the typical 120 mph. But I doubt it.

Even at 60 mph, half the typical 120 mph terminal velocity for an adult, that baby would land at 88 ft/sec and decelerate at such a rate upon impact that some serious forces would smash the kid. For example, F = m dv/dt ~ (W/g) 88 ft/sec^2 = (32 lb/32 ft/sec^2) 88 ft/sec^2 = 88 pounds of force upon impact. I assumed the weight of the baby was W = 32 lb and the impact lasted dt = 1 sec as the baby's 88 fps velocity screeched to a halt. (NB: dt = 1 sec is a conservative WAG. It's probably shorter, in which case F would be higher than the 88 lbs quesstimated here. The point is, even with a conservative estimate, it doesn't look good for the baby.)

88 pounds of force is survivable I would think. People do survive crashing at 60 mph in their cars. So, as you can see, if conditions are right, a baby might survive, but be badly banged up. But 176 pounds of force if the baby fell at a full 120 mph or so, is probably not survivable on the frail frame of a baby.

My guess is, if the accounts are true, the baby's fall was somehow cushioned so that the duration of the impact was drawn out, say, to two seconds for example. In my example, the force of the impact would have been reduced to 44 pounds for dt = 2, 44 lbs is just a bit over the weight of the 32 pound baby. I would think that's definitely survivable.

Another possibility is that the so-called "skyscraper" really wasn't. In which case the velocity of the fall on impact would be far less than 120 mph or even 60 mph. For example, v^2 = 1/2 gh; so that h = 2v^2/g = 2 (88)^2/32 ~ 450 ft, which is a bit less than a 60 story building. And at v = 88 fps upon impact (60 mph) that 32 pound baby might survive the fall if the targeted head gave on impact and increased the duration of that impact. But there are realtively few buildings at 60 or more stories. So lower "skyscapers" would result in impact velocities even less than 60 mph. In which case, the chances for survival would increase.

Good question. At first I thought a baby had no chance. But on crunching the numbers, I can see that under special conditions (long impact interval, lower skyscaper, or the drag characteristics of the baby), a baby might indeed survive.

The maximum speed of a falling object is it's terminal velocity. This is when the downward force of gravity exactly equals the upward force of air resistance, so there is no net force on the object, and it falls at a constant velocity.

The old observation that cats always seem to land on their feet has to do with the cat's terminal velocity. When falling from a great height (say, 5 stories), the cat can actually CHANGE it's terminal velocity by spreading it's legs to increase it's air resistance, thus slowing it down. They can actually fall from very high and run away unscathed.

Speed Of Gravity On Earth

Acceleration due to gravity is 9.8m/s^2, regardless of weight. Theoretically, a feather and an anvil should fall at the same speed. However, this could only occur in a vacuum where wind resistance is not present. So as the object falls, it continues to accelerate until other forces act upon it, such as the man stopping the baby's descent. Remember to take into account that this figure is in a vacuum, so wind resistance is not taken into account. I would have to assume that an object would continue to accelerate until impacting with another object.

Also, babies often survive falls as they do not realize they are falling and do not tense up before impacting with the ground. The relaxed state of their body absorbs the impact much better, thus lessening injuries sustained.

If there's no resistance and the object is in an extremely long vacuums then the theoretical top speed is the speed of light according to physics or 300,000 km/s. the gravity of earth would accelerate an object at 9.8m/s squared so it would take a while. If it's just falling through the atmosphere then the top speed would depend on the shape and weight of the object.

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RE:

What is the maximum speed of gravity on a falling object?

Like if you dropped a tennis ball from a great height... does it accelerate during it's decent... and reach a top-out speed of an average maximum velocity?

In simple terms please. (Average maximum velocity of gravity allowing for slight variations in objects which generate some.....

The maximum speed of a falling object (aka 'terminal velocity') occurs when the force due to gravity (9.8*m) is equal to the force due to air resistance (-.5*rho*v^2*A*Cd).

The average human male has a terminal velocity of about 55m/s (123mph). As for a baby? I would assume it is somewhat smaller.

On a side note, babies are much more flexible than adults. Their bones are not fully hardened, and can bend and twist to an extent without breaking (do not try this). This ability has evolved for this exact purpose (falling down, not specifically out of skyscrapers, but you get the idea).

Maximum velocity will be achieved when the force of gravity is balanced by the retarding force of wind resistance (or it hits something solid). Wind resistance increases with the square of speed - so resistance as 80mph will be four times the resistance at 40 mph. For a feather, with area being so much greater in proportion to weight, the wind resistance will cause terminal velocity to be reached at a much lower velocity than for, say, a falling baby!

the real question is does gravity have a terminal velocity? meaning will an object caught in gravity in space [this eliminates air resistance and friction] continue to accelerate to the speed of light or does it reach a maximum speed, and does the mass of the source of gravity influence velocity? say the difference between a black hole and our moon? kind of twists your noodle huh!

An object can reach a terminal velocity (or top speed) falling do to the friction (air resistance) around it. It depends on the object falling. If there was no friction, the object would continue accelerating until another force stopped it.