Is it possible for a horizontally running human to cover a certain distance faster than a vertically falling object in Earth's gravitational field?

Answer 1

it all depends on the terminal velocity of the falling object. Terminal velocity is when a falling object

experiences zero exceleration or basically when gravity and air resistence balance themselves out,

leaving the falling object at a limited speed. The terminal velocity of a feather would be very low and

could easily be outrun by a human but the terminal velocity of a brick would be much higher and

impossible to outrun. The approxtiamate terminal velocity of a human is 200 km/h or

120 miles/h which also could not be outrun by a human.

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The first answer was a good job, but the question is so interesting that I want a chance

to play with it too.

As the first one suggested, we can look at this in two general ways ... with air and

without air.

If air is present, then a terminal falling velocity exists, which depends on the shape,

size, and weight of the falling object, and the answer is indeterminate. For example, a

running man could easily beat the average descent rate of a hang glider, an autumn

leaf or a Schweizer sailplane.

If air is not present and the object is falling through a vacuum, then the answer is a lot more

precisely defined, and it's easy to calculate. An object that falls in Earth's gravitation starts

at zero speed, and accelerates at 9.8 meters per second2, whereas a human sprinter

explodes off the blocks almost instantly. So there's some period of time when the man

is running faster than the falling object, but since the falling object keeps gaining speed,

it eventually wins. We only have to calculate the 'break-even' distance.

Running man's top speed . . . Look at record times for 100-meter sprint, and then

let's take 10 meters per second as top human speed.

Falling object starting from zero speed . . . how long does it fall before its average

speed up to that time exceeds 10 meters per second ?

Average speed = 1/2 (Vinitial + Vfinal) = 10

Vinitial = 0

Vfinal = gT

1/2 (gT) = 10

gT = 20

T = 2.04 seconds

The running man is ahead on distance for the first 2.04 seconds after the object is dropped

(as long as he's in Usain Bolt's class, or close to it). At that time, the object catches up

to his distance, and is ahead of it after that.

The break-even distance is 20.4 meters. The man covers any distance less than that,

faster than the object can if its fall begins from rest. Any distance longer than 20.4 meters

is covered by a falling object faster than by a running man.

And that's the way I see it.

Answer 2

No, in Earth's gravitational field, a vertically falling object will reach the ground faster than a horizontally running human covering the same distance. This is because gravity accelerates the downward motion of the falling object, allowing it to reach the ground in a shorter time than the horizontal motion of the human.