physical significance

From: shashidhar (shashidhar.a_at_in.bosch.com)
Date: 12/13/04 

Date: Mon, 13 Dec 2004 18:33:11 +0530

Hello All,

I am a beginner in mathematics and i am stuck in the following concept i
found in a book of complex numbers:

"Consider a child throwing a ball into the air.

For example, assume that the ball is thrown straight up, with an initial

velocity of 9.8 meters per second. One second after it leaves the child's

hand, the ball has reached a height of 4.9 meters, and the acceleration of

gravity (9.8 meters per second2) has reduced its velocity to zero. The ball

then accelerates toward the ground, being caught by the child two seconds

after it was thrown. From basic physics equations, the height of the ball at

any instant of time is given by:

h = (-g*t^2)/2 + v*t

where h is the height above the ground (in meters), g is the acceleration of

gravity (9.8 meters per second2), v is the initial velocity (9.8 meters per

second), and t is the time (in seconds).

t ' 1± 1&h/4.9

Now, suppose we want to know when the ball passes a certain height.

Plugging in the known values and solving for t:

For instance, the ball is at a height of 3 meters twice: t =0.38 (going up)

and t = 1.62 seconds (going down).

As long as we ask reasonable questions, these equations give reasonable

answers. But what happens when we ask unreasonable questions? For

example: At what time does the ball reach a height of 10 meters? This

question has no answer in reality because the ball never reaches this
height.

Nevertheless, plugging the value of h = 10 into the above equation gives two

answers: t = 1+ sqrt(-1.041) and t = 1- sqrt(-1.041)."

My question is, in the above example what is the Physical significance of
the complex time?

I believe this quantity of complex time would be used in some physical
concept or theory....How do we analyse this complex time in the real world?

Thanx in advance.

Shashi

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