# Another free fall topic

1. Sep 1, 2010

### astenroo

Another free fall topic :)

Here I don't really know where to start

1. The problem statement, all variables and given/known data
A body in free fall covers 64% of the total distance fallen in the last second. From what height did it fall?

2. Relevant equations

y= y1 + y2, where y1=0,36y and y2=0,64y
y=.5at², where a=g=9.8 m/s²

and this is where I get stuck. In a tv-diagram it would be a straight line from origo, and the area under the line gives the distance fallen. And I'm still stuck. Utilizing the y=.5gt² would give me a parabola, and the area under the curve would give me the velocity with which it hits the ground, but I'm not sure whether that would help me much either.

3. The attempt at a solution

2. Sep 2, 2010

### CompuChip

Re: Another free fall topic :)

Suppose that the total distance fallen is h, and that tf is the total falling time.
Then you can fill in your formula for two time instances, namely tf and (tf - 1), for example:
h = (1/2) * 9.81 * tf
(where * stands for multiplication) and another one for t = tf - 1.

This will give you two formulas with two unknowns (h and tf) which you should be able to solve for.

3. Sep 2, 2010

### astenroo

Re: Another free fall topic :)

Ok, so

(1) h=1/2gtf² and
(2) 0,36h=1/2g(tf -1)² => h=13,61tf² - 27,25tf + 13,61 substitution into (1) which gives
8,71tf² -27,25tf + 13,61 => tf = 2,50s or 0,624s (can be ruled out since it doesn't make any sense)

tf = 2,50s gives h=1/2g*2,50²=30,625m. I wonder if I made this one too complicated...

4. Sep 2, 2010

### CompuChip

Re: Another free fall topic :)

Looks all right to me, except that I cannot clearly make out if you actually used (tf - 1)² = tf² - 2 tf + 1
rather than
(tf - 1)² = tf² - 1

Indeed the time interval < 1 second can be ruled out on physical grounds here.

I don't know if this is too complicated, it is the way that I would have done it though.

5. Sep 2, 2010

### astenroo

Re: Another free fall topic :)

I used (tf - 1)² = tf² - 2 tf + 1, which should be the correct way.

Thanks for the help
-alex