Help explaining a math problem.

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RandomSid

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Ok, wasn't sure where to put this but I need help explaining something.

The problem is that a train is moving in one direction at 70 miles per hour. A person is atop the train running in the opposite direction and not losing any ground(to a person watching from the side of the train on the ground it appears that the person running on top of the train is staying in the same location). How fast is the person atop the train running and how do you explain it through mathematics?
 
RandomSid said:
Ok, wasn't sure where to put this but I need help explaining something.

The problem is that a train is moving in one direction at 70 miles per hour. A person is atop the train running in the opposite direction and not losing any ground(to a person watching from the side of the train on the ground it appears that the person running on top of the train is staying in the same location). How fast is the person atop the train running and how do you explain it through mathematics?
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Let's mark a place as zero [the person watching from the side of the train] so that the distance the train travels is
DT = 70 * t
where DT is the distance from the person measured along the tracks and t is the time in hours. Now the persons distance, DP, from that same person, is the distance of the train minus the speed s the person is running in the opposite direction or
DP = 70 * t - s * t = (70 - s ) * t
or, since DP is zero
s = 70 mph.
 
Thank you. Now can you help explain why a person running down the inside of an aircraft traveling at 600 mph would not be running at 600 mph? I mean obviously the aircraft moving at 600 miles per hour, they would lose many many miles while running down the aircraft. But how to explain it in mathematical terms.
 
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RandomSid said:
Thank you. Now can you help explain why a person running down the inside of an aircraft traveling at 600 mph would not be running at 600 mph? I mean obviously the aircraft moving at 600 miles per hour, they would lose many many miles while running down the aircraft. But how to explain it in mathematical terms.
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The same equations apply. Pick your reference spot as a point to measure distance and the reference 'line' on which to measure distance and write the same equation. A person running down the center of a plane with 600 mph ground speed at 20 mph ground speed would have a net ground speed of 580 mph.
 
Denis said:
Huh?
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Basically, I was trying to explain how running against the momentum of a train while the train is moving 70 miles per hour and you not losing any ground would mean you were running at least 70 miles per hour. Then someone tried to say "I recently took a flight abroad. The plane was traveling at more than 600MPH. I quickly ran down to the other end of the plane to request more food from the flight attendant.Little did I know, that as I was running, I was technically running at more than 600MPH, thereby becoming the fastest man on the planet."​
 
RandomSid said:
Basically, I was trying to explain how running against the momentum of a train while the train is moving 70 miles per hour and you not losing any ground would mean you were running at least 70 miles per hour. Then someone tried to say "I recently took a flight abroad. The plane was traveling at more than 600MPH. I quickly ran down to the other end of the plane to request more food from the flight attendant.Little did I know, that as I was running, I was technically running at more than 600MPH, thereby becoming the fastest man on the planet."​
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He was not running at > 600 MPH - He was being carried at >600 Mph.
 
RandomSid said:
Thank you, I understand that, but I need help explaining it to someone else.
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If the case you gave (running in the direction of the aircraft heading) then the sign on the equations would be positive instead of negative and, in the example I gave (which was for running in the opposite direction), the ground speed in that case would be 620 mph. However, it does not mean that he was running that fast.
 
You have asked:
RandomSid said:
How fast is the person atop the train running and how do you explain it through mathematics?
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and
Now can you help explain why a person running down the inside of an aircraft traveling at 600 mph would not be running at 600 mph? I mean obviously the aircraft moving at 600 miles per hour, they would lose many many miles while running down the aircraft. But how to explain it in mathematical terms.
Click to expand...

But, in a situation like this, you cannot simply ask "how fast", you must ask "how fast relative to ...." and the answer depends upon what replaces the "..."! In the first case, where a person (Who is a remarkably fast runner, especially considering that he has jump between cars!) is running backwards, on a train that is moving 70 mph relative to the ground, is running at 0 mph relative to the ground and 70 mph relative to the train.

In the second problem, the person is "running down the aircraft" that is flying at 600 mph. A person sitting on the airplane is moving at 600 mph relative to the ground. A person that is running toward the front of the aircraft at 3 mph relative to the aircraft would be moving at 603 mph relative to the ground. A person running toward the tail of the aircraft at 3 mph relative to the aircraft would be moving at 597 mph relative to the ground.

(I might point out that I am NOT "explaining a math problem"! The only math required here is 600+ 3= 603 and 600- 3= 597 which, I am sure, you did not need explained. The fact that you must account for the point speed is "relative to" is a physics explanation,)
 
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Well

RandomSid said:
Basically, I was trying to explain how running against the momentum of a train while the train is moving 70 miles per hour and you not losing any ground would mean you were running at least 70 miles per hour. Then someone tried to say "I recently took a flight abroad. The plane was traveling at more than 600MPH. I quickly ran down to the other end of the plane to request more food from the flight attendant.Little did I know, that as I was running, I was technically running at more than 600MPH, thereby becoming the fastest man on the planet."​
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If we were in a court of law and I was defending the fastest man on earth proposition ... I would smooth my hair back and ask, was the man running? Yes! Ok then ...

With respect to the ground was the displacement accrued while he was running divided by the time interval of his run a figure over 600 mph. Yes!

Ah haw ... fastest running man off earth.

(and by the way, I have certain very valuable stock options you might be interested in ...)
 
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