Freefall-Type Question: Solving for Ball Catching and Building Length

[Iceman2032]

I am really struggling with this question:

A ball is dropped from the top of a tall building. Exactly 2 seconds later, another ball is thrown downwards from the top of the same building at 25 m/s. Will the second ball catch the first ball? If so, what is the minimum length of the building? If not, what is their closest approach?

I do not need the full solution, just a hint. It seems that whatever I do gets to a dead end. From the 5 variables (d, t, initial v, final v, and acceleration) I only have 2 of them in both cases...initial velocity and acceleration (which is 10 m/ss...given) I have also sketched the graphs but I just don't get this question.

Any help is appericiated.

 

[Chi Meson]

IF the 2nd one catches the first, then they would have the same displacement, wouldn't they? set two equations for d equal to each other and solve for time. If you get a negative answer, then "it can't happen."

 

[HallsofIvy]

distance fallen in t seconds is x(t)= (g/2)t²+ v₀t
where v₀ is the initial velocity.
The "dropped" ball has initial velocity 0, the thrown ball has initial velocity 25 (I'm taking positive downward). Also, be careful about when t= 0 is. If you take t= 0 to be when the first ball is dropped, the time the second ball is falling is t-2. The second ball will catch up to the two when they both have the same "x" so set up the two formulas, set them equal, and solve for t.

 

[Iceman2032]

Okay, I took your suggestions and came up with the calculations attached to this post.

First of all excuse the typos and all, I just noticed an 'is' needs to be an 'if'. Took me some time to convert my scribbles into a neat image.

Now as you can see I have ended up with a negactive value for x. Something tells me I'm doing something really wrong. I mean the value of x is supiciously small...and negative. According to the first reply, they should never catch.

Also in my answer sheet, the answer to this problem is indicated as: 180m

It doesn't say wether 180 is their closest approach or height of the building.

So can you please tell me what I am doing wrong? Am I even using the right formula?! And after I calculate x, where do I go from there?

I really get lost in these 'catch' problems...

 

[Iceman2032]

Nevermind, problem solved :)