Finding Maximum Height of Two Simultaneously Launched Balls

[EHogeberg]

This problem has been giving me problems for the past two days and I can't figure it out :( please help. this is my first ever physics class.

Homework Statement

A rubber ball is shot straight up from the ground with speed v_0. Simultaneously, a second rubber ball at height h directly above the first ball is dropped from rest.

Known:
V_0 and Height of original ball drop
y_coll= h- ((gh^2)/(2v_0)^2)
find:
h_max

Homework Equations

Vx= Vxi+ax (tf-ti)
Xf=Xi + Vxi + 1/2 ax (tf-ti)^2
Vxf^2= Vxi^2+ 2ax (Xf-Xi)

The Attempt at a Solution

I got to the point where I found what I thought was h_max and got

hmax= (V_0^2/g)- 1/2*V_0^2

the website I am working on told me I am missing a term but I can't figure out what I am missing. :(

 

[gneill]

The question is, what is the question? You didn't state what it is you're trying to find!

 

[EHogeberg]

how to find h_max

 

[gneill]

how to find h_max

Yes, but what is h_max supposed to represent?

 

[EHogeberg]

the maximum value of h for which a collision occurs before the first ball falls back to the ground?

 

[SammyS]

the maximum value of h for which a collision occurs before the first ball falls back to the ground?

I would have never guessed that.

 

[SammyS]

If a ball is shot vertically upward, with initial velocity, v₀, how long does it take the ball to return to its initial location?

 

[EHogeberg]

I know this book and website combination is not the most helpful thing in the world. Whaat I have done so far is pluged in Hmax for the Xf of the second kinematic equation and when I solved it I ended up getting v_0^2/g-1/2 v_o^2 which got me to where it said I was close but I was either missing a term or it was incorrect and I can't figure out what's wrong so I guess my question should be...what am I doing wrong

 

[EHogeberg]

If a ball is shot vertically upward, with initial velocity, v₀, how long does it take the ball to return to its initial location?

sorry I didnt see that question...I am not sure the only thing I can think of is time final-time initial but that wouldn't help me. I really don't knowfrom what I can think of it would equal the velocity over the gravity

 

[SammyS]

sorry I didnt see that question...I am not sure the only thing I can think of is time final-time initial but that wouldn't help me. I really don't know

from what I can think of it would equal the velocity over the gravity

If it wouldn't help, I wouldn't have asked it. It will definitely help to work that out.

 

[EHogeberg]

what I meant to say is my answer wasnt going to help me sorry for the unclarity

 

[EHogeberg]

I finnaly figured it out...thank you guys for the guidence

 

[SammyS]

Good. The collision should occur just before the first rubber gets back to ground level.

 

[EHogeberg]

yeah that's what I got