# Homework Help: Initial velocity of ball B hit a free falling ball A

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1. Jan 1, 2018

### Bond

1. The problem statement, all variables and given/known data
A boy release ball A from height 5m from ground at the same time other boy throw ball B vertically upward to exactly strike ball A. When ball B released it was 1m from ground find minimum initial velocity of ball b. Given g=10m/s^2
a) 2m/s b) 3m/s c) 4m/s d) 5m/s

2. Relevant equations
x (t) = v0t+1/2at^2

3. The attempt at a solution
From the problem distance between each ball is 4m when it was released and both was released at same time so when it strike each other time must be equal
Then i let x be the distance ball A travel and 4-x be distance ball B travel so i got.
x=1/2gt^2 = 5t^2 since ball A was released it has no initial velocity
and 4-x=v0t-1/2gt^2=v0t-5t^2
Solve for both I got ut =4 then I stuck here then I substitude value from choice and got 5 (the exact is about 4.4) so is there any real way to solve this
P.S. I try using energy conservation and end up with 0=0 all time.

Sorry if the problem look weird since I translate it from my own language

2. Jan 1, 2018

### BvU

Hello Bond,

yes, your exercise text puzzles me: what if boy B just holds te ball ? Then ball A will also strike ball B exactly ?

Or does it say that the balls hit each other exactly half way ?

3. Jan 1, 2018

### Bond

It doesn't say where they hit but I'm very sure that the ball B has to be thrown and hit ball A mid air because they were released at the same time

4. Jan 1, 2018

### PeroK

I reckon they have to collide before ball B hits the ground. That's where the minimum velocity comes in.

5. Jan 1, 2018

### PeroK

Some of your equations have $g$ in them and some don't. Is that a typo?

You need to think about displacements rather than distances here. Also, I would set the ground as $x = 0$ and use that as my reference frame.

That said, $ut = 4m$ is correct. Now, you need an idea about how to calculate the minimum $u$ from that. Hint: if $u$ is a minimum, what is $t$?

6. Jan 1, 2018

### Bond

So it mean that t should be maximum which is the time ball A take to hit the ground is that correct?

7. Jan 1, 2018

### PeroK

That's right.

8. Jan 1, 2018

### Bond

Thanks a lot

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