Expert: Stephen King - 10/23/2004

Question
I need your help with 2 word problems you have to use quadratic equations to solve problems step by step.

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.

2. x varies directly as the sqaure of s and inversely as t. How does x change when s is doubled when both s and t are doubled.

Answer
Hello Lindsey.

1.  "directly proportional" means multiplied by a constant.  So translate the words into math symbols:

Let d=distance
Let t=time

d=a*t^2
Solve for a:
1296=a*6^2
a=36

Now plug the a back into d=a*t^2 for the new distance to solve for time.

2304=36*t^2
64=t^2
t=8 or t=-8

Since time is never negative, we can discard the -8.  So it will take 8 seconds for the object to fall.

2.  x=(a*s^2)/t
multiply by the constant because it's proportional, and divide by t since it's inversely proportional.

For the changes on x, plug in 2s for s:
x=(a*(2s)^2)/t
A 4 factors out in the numerator, so we now have:
x=(a*4(s^2))/t
so x quadruples, or is 4 times larger.

Now for the doubling of s and t:
x=(a*(2s)^2)/(2t)
Now there's a 2 in the denominator:
x=(a*2(s^2))/t
so x doubles, or is 2 times larger.

Steve