Settle a bet: if a guy ran full-speed and leapt off a 7-story roof, how far out from the bldg would he land?

Question

This has been a long standing question debate among friends in an office building. If the guy is around 6 feet tall, 190 lbs and ran at his maximum speed, how far could he reasonably be expected to land away from the building?

Answer 1

All right, say he's a great runner - 4-minute-mile guy. He's going about 22 feet per second, then, when he takes off.

It's gonna take about 2.1 seconds* before the splat, so he's gonna be about 46.2 feet from the building at impact.

*Figure standard Earth gravity - 32 ft/sec sq. Figure 7 stories = 70 ft.

Note (edit) are these other guys just guessing, or what? Sheesh. It's just physics, people. And, yeah, the resistance of the air figures in, but it figures in both factors, so it doesn't really matter.

Answer 2

If the man is jumping off the building in a vacuum...

The time it would take him to hit the ground would be equal to

sqrt((hight*2)/(accelloration)) =time

so if the building is 70 feet high and the acceloration of gravity was 33ft/s^2, it would take right at 2 seconds to hit the ground.

if he was running across the building at full speed, say 20 feet/second (~13 miles per hour), he would land ~40 feet from the building.

The mass of the man would not matter.

Now if you want to talk about the impulse when he hits the ground that is interesting. Impulse = mass * velocity. That means that a 190 lbs man would hit the ground going 66 feet per second (45 miles/hour). That means that he would hit the ground with ~ 12000 lbs of force! That would hurt.

If the man jumps off an actual building on the Earth with an atmosphere, many things would change. Is he jumping into the wind or with it?

Answer 3

Simple! 44.917197485 feet. (45 feet) That is, if the guy is average 6 feet tall, 190 pounds, no wind, in Atlanta, or Cleveland, and had just eaten 2.235 scoops of vanilla HAAgen Dazs ice cream on a Tuesday. Just kidding! Blue Bell milk chocolate ice cream would have the same results. Question: Why'd he jump?

Answer 4

Assuming velocity of 15 mph in x direction and 0 in y direction, and 10 ft per floor (70 ft), mass is unimportant. My estimate is 45 feet from edge of roof. He will hit the ground going over 64 mph. SPLAT!

Answer 5

I'd say not much more than if he just ran and jumped on the ground, maybe 2 or 3 feet more. The parabola would go very vertical very quickly .

Answer 6

Not much farther than if he simply jumped from point A to
point B on the ground..
The 7 story building make very little difference..
Human bodies do not glide very good...

Answer 7

It depends, is the building on the moon or on earth?

Just kidding, but I'd guess just a few feet from the wall...force of gravity is going to pull him down fast unless he is farting out rocket fuel.

Answer 8

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Answer 9

8+'