Negative Time: A Puzzling Physics Problem

[vissh]

Q.)A stone is dropped from a balloon going up with a uniform velocity of 5.0 m/s . If the balloon was 50m high when the stone was dropped, find the time after which the stone will be at ground.

Ans)On solving this, we can get a quadratic equation in 't'[time]. The 2 values of t was then found to be (1 +(41)^1/2)/2 and (1 -(41)^1/2)/2 i.e. t = 3.7s , -2.7s.
The time can't be negative as i thought And book also has 3.7s as answer .
...The thing over which i was wondering is that its written in book " Negative t has no significance in this problem ". Can in any case the -ve value to time can have physical significance ?

Was just curious abt it :)

 

[AC130Nav]

Mathematics is not physics; that's why we have experiments.

Or to put in mathematical terms, you often develop restrictions such as x cannot equal zero (where division by x occurs) that is carried on in solving an equation. In physics there are restrictions that are not always apparent in the math. You have one that, at least, is recognized.

Math is not the real world. It is a way of dealing with the real world but has its own limits.

 

[vissh]

Hehe thanks for reply :)
Got it :)
So, in physics -ve time got no physical significance .

 

[diazona]

Well, no, actually it can have a physical significance. In any physical situation, you have to pick (or be given) some event to mark time 0. Positive values of t describe events that happen after that "zero mark," and negative values of t describe events that happen before the "zero mark." So in any case where something happens before the event that you chose to mark t=0, its time will be negative.

For example, look at your problem. It tells you that the stone was dropped at time 0, but the equation doesn't "know" that. The only information that you plug into the equation is that, at t=0, the stone was 50 m high and was moving upwards at 5 m/s. Now, if that's all the information you had (50 m high, moving up at 5 m/s), you wouldn't know whether the stone was dropped or had been thrown up from the ground earlier. Same with the equation. So it gives you both possibilities: a positive solution to indicate when the stone will hit the ground after t=0, and a negative solution to indicate when the stone would have been on the ground before t=0 (if it had been thrown). Of course, it's up to you to read the problem and see that the stone only starting falling at t=0, so the t=-2.7s solution doesn't correspond to what really happened.

 

[AC130Nav]

It is valid (in the mathematical sense) to say that the fall of the stone can be modeled on an axis of time as a parbola, the second solution being the UNREAL situation being when it was going up.

If you use enough of these unreal solutions, you end up with the Hawking universe(s).

 

[vissh]

Thanks Ac and diazona >:D