Posted: 2/9/2012 6:17:40 PM EDT
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Wife and i are here in vegas and got into a debate on how long (time) it woild take for someone to hit the ground if a person were to jump.off the cosmopolitan.
Building is 603.5 feet. Object is 5"10 180 lbs |
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6.14 seconds
Edited for explanation: I have no idea what the official formula is, so I had to come up with it from scratch while drunk, using logic to figure out the algebra. Here was my line of thinking: Assuming no air resistance, things accelerate at 32 feet per second per second. So given a timeframe, the average speed would be the time in seconds times 32 divided by 2. Put another way, velocity = 32x / 2 where x is the number of seconds. We need to make the average speed times x equal to 603.5. So the equation for that would be x(32x / 2) = 603.5 If you simplify that, it becomes 16x^2 = 603.5. Divide both sides by 16 and you get x^2 = 38.34375. Find the square root of both sides and you get x = 6.14. |
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Velocity with respect to time
The general gravity equation for velocity with respect to time is: v = gt + vi (See Derivation of Velocity-Time Gravity Equations for details of the derivation.) Since the initial velocity vi = 0 for an object that is simply falling, the equation reduces to: v = gt where v is the vertical velocity of the object in meters/second (m/s) or feet/second (ft/s) g is the acceleration due to gravity (9.8 m/s2 or 32 ft/s2) t is the time in seconds (s) that the object has fallen EDIT: Fuck it, it's already been solved. 
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x = x1 + V1t + 1/2gt^2
0 = 603.5 + 0 + 1/2(-32.2)t^2 solving for t 6.122 seconds in free fall neglecting air resistance. Actual time would be a bit longer. Hitting the ground at v = v1 + at 197 fps or ~ 134 mph, which I believe is still under terminal velocity for a human in parachute-style free-fall. |
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It's easy to solve if you neglect air resistance. As has been demonstrated. Throw in air resistance (which can make the number vary) and it's a pretty tough cookie. There is air resistance I know, that's why nobody here will solve it exactly. If I had to give a WAG, I would say the actual time would be around 7.5 seconds. |
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Is there a app where you can punch in the numbers or did you do it by hand? Also was it taken into account that they dont start falling at terminal velocity? How long does it take to reach terminal velocity? I just did it by hand. I have my calculator sittin in front of me. Taking a break from thermo homework
Initial velocity = 0 We could take air resistance in to account, but then it becomes a differential equation instead of a simple plug and chug. You'd also need a drag constant, which I have no idea where to look up a realistic drag coefficient for a human in free-fall. I COULD calculate it, should someone find a drag coefficient I believe terminal velocity for a human is ~150 mph, but varies based on several parameters like your orientation in the air, mass of the person, surface area, etc. 150 mph is roughly equal to 220 fps To get to that in free fall with no air resistance, 220 = 0 + (32.2 ft/s^2)(t), solving for t = 6.83 seconds |
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It's easy to solve if you neglect air resistance. As has been demonstrated. Throw in air resistance (which can make the number vary) and it's a pretty tough cookie. There is air resistance Depends on body position, then. Going into skydiver mode can slow you down a tad. |
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Quoted:
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Is there a app where you can punch in the numbers or did you do it by hand? Also was it taken into account that they dont start falling at terminal velocity? How long does it take to reach terminal velocity? I just did it by hand. I have my calculator sittin in front of me. Taking a break from thermo homework
Initial velocity = 0 We could take air resistance in to account, but then it becomes a differential equation instead of a simple plug and chug. You'd also need a drag constant, which I have no idea where to look up a realistic drag coefficient for a human in free-fall. I COULD calculate it, should someone find a drag coefficient I believe terminal velocity for a human is ~150 mph, but varies based on several parameters like your orientation in the air, mass of the person, surface area, etc. 150 mph is roughly equal to 220 fps To get to that in free fall with no air resistance, 220 = 0 + (32.2 ft/s^2)(t), solving for t = 6.83 seconds I thoughy it was 120mph |
| This is a simple problem if you ignore atmospheric drag and only consider gravitational aceleration. But, that would not give you an accurate answer. It depends on your clothing, how you tumble, etc. You will need to try it and measure the elapsed time. Best to make a video. |