# Kinematics, One Dimension, Acceleration, 2 objects problem

## Homework Statement

Ball A is dropped from the top of a building of height h at the same instant that ball B is thrown vertically upward from the ground. At what height will the balls collide if the collision occurs when the balls are moving in the same direction and the speed of A is 4 times that of B.

VA0 = 0 - the internal speed of ball A.
h=h; a=g;
tc - the time when the balls collide.
VA(tc)=4*VB(tc)

## Homework Equations

[/B]
v = v(initial) +at
x = x(initial) + v(initial)t + (at^2)/2

## The Attempt at a Solution

XA(tc)=XB(tc)=hc (height whenn the balls collide)

XA(tc)= h-(g*(tc)2)/2

XB(tc)= XB(tb) - XB(tb→tc)=
=VBO - (g*(tb)2)/2 - (g*(tc-tb)2)/2=
=VBO - (g*(tb)2) - (g*(tc)2)/2 + g*tc*tb
V(tb)=0 ⇒VB0=g*tb⇒
⇒XB(tc)=g*tc*tb - (g*(tc)2)/2

XA(tc)=XB(tc)= h=g*tc*tb

VA(tc)=4*VB(tc) ⇒ -g*tc = -g*(tc-tb) ⇒ 3tc= 4tb →witch is impossible!

TSny
Homework Helper
Gold Member
Hello and welcome to PF!

XB(tc)= XB(tb) - XB(tb→tc)=
=VBO - (g*(tb)2)/2 - (g*(tc-tb)2)/2=
I'm guessing that tb denotes the time at which B reaches maximum height. So, you are breaking up B's flight into two parts: the upward moving part and the downward moving part. It's not wrong to do this, but there is no need to break it up. The acceleration of B is constant throughout its entire flight. So, you can use the equation XB = VB0t - (g/2)t2 for the entire interval from t = 0 to t = tc.

The mistake you made is in the second line quoted above where VBO should be multiplied by a time.

Spoti112
Hello and welcome to PF!

I'm guessing that tb denotes the time at which B reaches maximum height. So, you are breaking up B's flight into two parts: the upward moving part and the downward moving part. It's not wrong to do this, but there is no need to break it up. The acceleration of B is constant throughout its entire flight. So, you can use the equation XB = VB0t - (g/2)t2 for the entire interval from t = 0 to t = tc.

The mistake you made is in the second line quoted above where VBO should be multiplied by a time.
Hello and welcome to PF!

I'm guessing that tb denotes the time at which B reaches maximum height. So, you are breaking up B's flight into two parts: the upward moving part and the downward moving part. It's not wrong to do this, but there is no need to break it up. The acceleration of B is constant throughout its entire flight. So, you can use the equation XB = VB0t - (g/2)t2 for the entire interval from t = 0 to t = tc.

The mistake you made is in the second line quoted above where VBO should be multiplied by a time.
thank you very much! I got the correct answer. <3
p.s. sorry that i didn't clarified what tb means

TSny
Homework Helper
Gold Member
OK. Good work.