Solve Ball Drop Problem: Find Initial Velocity

[minhngo]

Hi, I appreciate it if someone can reply and help me out with this problem.

A ball is thrown straight up from the edge of the roof of a building. A second ball is dropped from the roof 1 second later. Air resistance may be ignored.

(a) If the height of the building is H m, what must be the initial speed of the first ball if both are to hit the ground at the same time?

So far I understand that there is:

X(t)=H+Vo(T+1)+1/2(-9.8)(T+1)^2 -> first ball

X(t)=H+1/2(-9.8)(T)^2 -> second ball

Then I know that the two formulas equal each other. From there I found T=(Vo+4.9)/(Vo-9.8)
This is where I get stuck.

 

[zwtipp05]

You should use T instead of T+1 for the second ball since it is dropped one second after ball one.

 

[minhngo]

Sorry that was a typo. I'll fix it.

 

[Fermat]

From the 2nd eqn, you can get T in terms of H.

Substitute for T into the expression you got stuck on.

 

[VietDao29]

...
X(t)=H+Vo(T+1)+1/2(-9.8)(T+1)^2 -> first ball

X(t)=H+1/2(-9.8)(T)^2 -> second ball

Then I know that the two formulas equal each other. From there I found T=(Vo+4.9)/(Vo-9.8)
This is where I get stuck.

I don't really know what you mean by 'the two formulas equal each other'...
You know that when the second ball hits the ground, the first ball will also hit the ground, you have the height, the acceleration, and the initial velocity of the first ball (0 m / s). Can you find how long it takes the second ball to reach the ground? Let say it takes t (seconds) for the second ball to reach the ground.
From there, you know that it takes (t + 1) seconds for the first ball to reach the ground.
You have the first ball initial height, its acceleration, and you know how long it takes to reach the ground. Can you find its initial velocity?
Viet Dao,

 

[minhngo]

What I meant to say was equation is that I set up:

H+Vo(T+1)+1/2(-9.8)(T+1)^2=H+1/2(-9.8)(T)^2

And from there I found T. However I am having trouble finding Vo.

 

[Fermat]

You can get Vo by substituting in for T in terms of H

 

[minhngo]

OK, I am a little confused. If I substitute T in T=(Vo+4.9)/(Vo-9.8) in terms of H, I would still have two variables, Vo and H.

 

[Fermat]

That's right. Your final expression will give Vo as a function of H.

Consider H as an (unknown) constant.

 

[minhngo]

Oh! thanks. I understand now.