Calculating Building Height Using the Quadratic Formula

[ssb]

Homework Statement

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.

Homework Equations

Quadratic formula
physics

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? I am only used to there being 3 terms in the poly nomial (like x^2 + x + 4). I am thinking I have to combine the -(2TH/Vs) and -2H/g somehow but I don't know how! Please help!

 

[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.

 

[ssb]

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.

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.

 

[hage567]

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