# Simple position-time function question

1. Aug 12, 2012

### tarkovsky

1. The problem statement, all variables and given/known data
A stone falls freely down a well. 1.6 seconds later, another stone is cast 25m/s in a straight line, down the well. The two stones hit the bottom of the well at exactly the same time. How deep is the well?

ag=9.8 m/s2

2. Relevant equations

x=x0+v0+1/2at2

3. The attempt at a solution
Assuming x0=0 for both stones and that a/2 is 4.9, my work is as follows

(4.9m/s2)t2=(25m/s)(t-1.6)+(4.9m/s2)(t-1.6)2

Essentially I wanted to find at what point the graphs would intersect. I believe my set up is correct, my problem was solving for the variable t. I was unable to solve for t and was forced to used wolfram to discover the approximate value for t which would represent the total duration for both rocks to strike the ground. I found t≈2.94592s which, when plugged into both equations yielded a result equal at 4 significant figures past the decimal point. x≈42.5243m

Therefore the wells is approximately 42.5243 meters deep.

Is there anyway to solve for x without resorting to wolfram?

2. Aug 12, 2012

### tiny-tim

welcome to pf!

hi tarkovsky! welcome to pf!
now expand the brackets, and rewrite in the standard quadratic equation form, ax2 + bx + c = 0

3. Aug 12, 2012

### PeterO

What tiny-tim suggested - then consider the following.