Expert: Richard J. Raridon - 10/7/2006

Question
I don't mean to be a pain, but i'm not sure I understand the answer to question one. Could you explain it just a little? Thanks.
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Followup To

Question -
Hi, I've got two word problems I guess i just don't get.

Question 1:

The distance an object falls is directly proportional to the square of the time it has been falling. After 6 seconds it has fallen 1296 feet. How long will it take to fall 2304 feet?

Question 2:

x varies directly as the square of s and inversely as t. How does x change when s is doubled? When both s and t are doubled?

I heard you guys are good.

Thanks.

Answer -
1- S = at^2 so 1296 = a(36) and a = 36
2304 = 36t^2 so t = 8s
2- x = as^2/t
when s is doubled, x increases by a factor of 4
when both are doubled, x increases by a factor of 2.

Answer
If the distance is directly proportional to the square of the time, then the equation is S = at^2 where a is a constant.  You can evaluate a since you know S and t for one case.  Therefore, you have the equation S = 36t^2 and you can put in a value for S or t and calculate the other variable.  
If this object were falling near Earth the equation would be S = 16t^2, where 16 equals (1/2)g.