# 1D Kinematics Easy

1. Sep 7, 2011

1. The problem statement, all variables and given/known data
A rubber ball is shot straight up from the ground with speed vo. Simultaneously, a second rubber ball at height h directly above the first ball is dropped from rest.

At what height above the ground do the balls collide? Your answer will be a symbolic expressions in terms of vo and g.

2. Relevant equations
v=v0+at
x=x0+v0t+(1/2)at2
v2=v20+2aΔx

3. The attempt at a solution
For the first ball, I have $$v_f = \sqrt{v^2_o+2g}$$
For the second ball (which I think I have wrong), I have $$v_f = \sqrt{2(g)(-h)}$$

Unfortunately I'm not really sure where to go from here, or if I'm even headed in the right direction in the first place. Can someone please help?

Thanks.
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. Sep 7, 2011

### ehild

For both balls, write up the time-dependence of height in terms of the initial position and velocity (your second equation) . When they meet, their heights are equal: that means an equation for the time. Solve, and determine the height with the result.

ehild

3. Sep 7, 2011

First ball y=vot + .5(g)(t^2) second ball y=h+.5(g)(t^2). Am I solving for the wrong variable (you mentioned time)? Also does the derivative come into play? Sorry for all the questions, I've been up for a long time .

EDIT: Do you set them equal to each other?
h+.5gt^2 = vot + .5gt^2
h = vot
t = h/vo

??

4. Sep 7, 2011

### ehild

Are you sure that the sign of g is correct? If it is taken positive, will the balls fall to the ground at all?

ehild