# Calculate the velocity of the eight ball after collision

1. Jun 19, 2006

### aarietta

Hello, I was just wondering if I am doing this question correctly, if not, any suggestions please and thank you

A person takes aim at the eight bal in a game of billiards. Her shot gives the cue ball a velocity of 2.5m/s [forward]. The cue ball strikes the eight ball and continues with a velocity of 2.5 x 10^-1 m/s [forward]. If the mass of the cue ball equals the mass of the eight ball equals 400g, calculate the velocity of the eight ball after collision.

v1 of cueball = 2.5m/s [forward]
v2 of cueball = 2.5 x 10^1 m/s [forward]
m = 400g = .4kg

P1 = m1v1
P1 = 0.4(2.5)
P1 = 1 m/s

P2 = m2v2
P2 = 0.4(2.5 x 10^1)
P2 = 0.1 m/s

Ptotal = [(0.1)^2 + (1)^2]sqaure root
Ptotal = 1.0 m/s

Pafter = m1v1 + m2v2
1 = (0.4kg + 0.4kg)v
v = 1/0.8
v = 1.25 m/s

Thanks!

2. Jun 19, 2006

### neutrino

I don't get this. The total initial momentum of the system is just that of the cue ball before collision.

The problem does not state the balls move together after the collision.

3. Jun 19, 2006

### mark126

Hello,

I think you've made one small error on this question, in your equations it appears that you're looking for 1 velocity, when you're really looking for two. Your equation should look like this:

(0.4)(2.5) = (0.4)(0.25) + (0.4)V2prime

You already know one velocity, and you're searching for another (V2 prime) so you can't combine the two sections together (0.4+0.4)V2,
they must be seperate.

4. Jul 10, 2006

### thiotimoline

By conservation of total momentum,

Initial momentum = Final momentum (for any forms of collisions)
Initial P of cueball + Initial P of 8-ball = Final P of cueball + Final P of 8-ball
0.4(2.5) + 0 = 0.4(0.25) + 0.4v
v = 2.25ms

5. Jul 10, 2006

### arunbg

Please don't post full solutions .
You may suggest hints or point out where the OP is going wrong, but let him do it on his own .

6. Jul 10, 2006

### deepakalways

"A person takes aim at the eight bal in a game of billiards. Her shot gives the cue ball a velocity of 2.5m/s [forward]. The cue ball strikes the eight ball and continues with a velocity of 2.5 x 10^-1 m/s [forward]. If the mass of the cue ball equals the mass of the eight ball equals 400g, calculate the velocity of the eight ball after collision"

the eight ball is supposed to move forward.
let "m" be the mass of each ball(the value is crap), which is given to be equal for both.
conserving momentum in the forward direction,

m*2.5 + m*0 = m*0.25 + m* v
* denotes multiplication and v to be found.

cancelling "m" on both sides,

v+0.25=2.5