# Homework Help: Quadratic formula problem

1. Apr 11, 2007

### ssb

1. The problem statement, all variables and given/known data

A physics student with too much free time drops a watermelon from the roof of a building height H. He hears the sound of the watermelon going "splat" after a time interval of Delta T.
You may ignore air resistance. How high is the building? The speed of sound is Vs.

2. Relevant equations

physics

3. The attempt at a solution

Ok T = T1 +T2 = H/Vs + sqrt(2H/g)

(T - H/Vs)^2 = 2H/g

Therefore

T^2 - (2TH/Vs) + (H/Vs)^2 - 2H/g = 0

I want to solve for H.
How do I plug this into the quadratic formula so that I can solve for H? Im only used to there being 3 terms in the poly nomial (like x^2 + x + 4). Im thinking I have to combine the -(2TH/Vs) and -2H/g somehow but I dont know how!!!!! Please help!

2. Apr 11, 2007

### hage567

Yes, you combine the two terms, and take out the H. That will leave you with three terms in the form of a quadratic equation.

3. Apr 11, 2007

### ssb

Ok I combined them and got H (-2t/Vs - 2/g)

So tell me if this is correct

a = 1/Vs

b = (-2t/Vs - 2/g)

c = t^2

Because when I plug that in as an answer it comes back wrong.

4. Apr 11, 2007

### hage567

One thing I see is that a should be 1/Vs^2.