# Homework Help: System of Equations Mechanics problem

1. Sep 6, 2005

### Punchlinegirl

The x-coordinates of two objects moving along the x-axis are given below as a function of time t. $$x_1$$ and $$x_2$$ never have the same value. Calculate the value of $$x_2$$ when the objects are nearest to each other.
$$x_1$$= 23.0t
$$x_2= -28.0 +43.0t-8.0t^2$$

I solved the first equation for t, and then plugged it into the second one to get $$x_2= -28.0 + 43.0( \frac {x_1}{23}) -8.0(\frac {x_1}{23})^2$$

I tried to use the quadratic formula but got a negative number... can someone tell me what I'm doing wrong? Thanks in advance.

2. Sep 6, 2005

### lightgrav

it's easier algebra to replace those "x1/23" terms with "t".

This is a relative location question ... what is x2 rel. to x1?
now there's only one equation, one unknown (t).
minimize x2-x1 , by setting t-derivitive =0.

3. Sep 7, 2005

### HallsofIvy

If you mean you completed the square to find the minimum value of the quadratic then, since that quadratic is equal to x2, you are just finding the minimum value of x2 itself, not where the distance between x1 and x2 is a minimum.

The distance between x1 and x2 is |x1- x2|- that's what you want to minimize.

It's probably simplest to look at x1- x2 and x2- x1 separately.

4. Sep 7, 2005

### Punchlinegirl

Ok I got it... thanks for your help