How to Calculate Building Height Using Speed of Sound and Physics Equations

[Crush1986]

Homework Statement

A physics student with too much free time drops a water melon from the roof of a building. He hears the sound of the watermelon going "splat" 2.50s later. How high is the building? the speed of sound is 340 m/s. Ignore air resistance.

Homework Equations

D= Vt (to find how fast sound travels from ground back)

X= Xo + 1/2*(Vo+V)*t

Vf = Vo +a*t

The Attempt at a Solution

So I did everything right except one thing. I calculated the height of the building by finding
y= 340m/s*(2.5-t) *t here being time of the melon hitting the ground. I thought Vf was going to equal -9.8t, found by subbing all known info into the equation Vf = Vo +a*t, it turns out that this portion of information must be positive to get the correct answer though it seems.

When all was said and done I tried to solve the problem for time of fall with,
-4.9t^2 + 340t - 850 = 0, this is not the correct formula though to obtain the correct fall time. I found that it has to be, 4.9t^2 + 340t - 850 = 0.

I just can't logically see why the first term is not negative. In the person's answer I was looking at they had, " -y = -1/2*g*t^2 and that simplifying down to y = 4.9t^2.

I just want to see this problem correctly. I'm learning all this on my own to kind of have a head start next semester. I think it's very important that I get the concepts down in stone and can interpret diagrams with no problem.

Thanks for any help! If you need anymore info I can provide it.

 

[Pythagorean]

Tell us why you think this is valid:

y= 340m/s*(2.5-t) *t

and what starting equation it comes from.

 

[mfb]

You are mixing two different times here (both are called "t" in your equations), the time for the melon to fall down and the time the sound travels from the floor to you.

 

[Crush1986]

Tell us why you think this is valid:

y= 340m/s*(2.5-t) *t

and what starting equation it comes from.

Sorry the, "*t" isn't supposed to be part of that. I was trying to say y = 340m/s * (2.5 - t), where t is the time of impact. I see now my choice to use an asterisk was a poor one. The equation is in the form D = Vt, this was to solve for the height of the building the 2.5-t was to find the time of the sound wave took to travel from the ground to the top of the building.

 

[Crush1986]

You are mixing two different times here (both are called "t" in your equations), the time for the melon to fall down and the time the sound travels from the floor to you.

I thought I had that correct. The only problem I saw here was the sign of the coefficient for the first part of my final equation. I just don't see how the final velocity isn't negative. I tried to say which t was which.. I did do it poorly. I should just label one t1 and t2 maybe for my posts here.

 

[mfb]

Well the final equation is a quadratic equation with two solutions, one physical with a positive velocity and one unphysical with a negative one (this would correspond to a cannon, shooting the melon upwards and emitting sound at the same time).

 

[Crush1986]

Well the final equation is a quadratic equation with two solutions, one physical with a positive velocity and one unphysical with a negative one (this would correspond to a cannon, shooting the melon upwards and emitting sound at the same time).

I know. Really I just want to know why the 4.9t^2 is correct and -4.9t^2 is wrong. I get that for Vf which makes sense. It's a negative velocity because the melon is moving down to Earth and I chose up as my positive y axis.

To get V = -9.8t I used Vf = Vo + at , so, Vf = (0 m/s) + -9.8t again I think it should be negative because the acceleration is downward relative to my perameters.

I then plugged this into the equation Y = Yo + 1/2 * (Vf + Vo) *t, along with the variable for the Y that 340 (2.5-t) where t was the time of impact in this equation.

Lol this is almost scary. I'm in bed away from the books remembering all this perfectly.. This stuff bothers me too much. Haha.

 

[Crush1986]

Ok I had an epiphany while dozing off 340(2.5-t) is a positive number, setting it equal to -4.9t^2 isn't possible. It would have to be a positive coefficient. I just don't see how the pure math shows it. Am I missing something? Is using logic here at this step the only way? If so, I feel there could be infinite pitfalls to watch for at every step of problems like these... Scary. Help?

 

[Crush1986]

I got it I think! I subbed in the height of the building on the left. Yah that is positive but the right side of the equation is for the fall a negative number! The left should be the height of the building but negative to correspond with the fall... I had apples on one side and oranges in the other I suppose... K NOW I can go to sleep.