Question

A cue ball initiallymoving at 4.2m/s strikes
a stationary eight ball of the same size and
mass. After the collision, the cue ball’s final
speed is 2.2 m/s .

Find the cue ball’s angle  with respect to
its original line of motion. Consider this to
be an elastic collision (ignoring friction and
rotational motion).
Answer in units of degrees

Answer 1

hmmm seems to be more of a physics question than mathematics...

Answer 2

lets see...

Answer 3

You can do it @piglet9 . You'll get to 99 in no time.

Answer 4

:o thanks..i'm trying to think about my physics days long time ago...

a purely elastic collision would transfer the entire velocity to the other mass if hit straight on, so this does have an angle...

Answer 5

But if you want a hint. First figure out the energy of the cue ball. Find the energy of the 8 ball, the difference is the remaining energy in the cue ball since the collision is elastic.

Answer 6

energy of cue ball = 0.5mv^2?

energy of 8 ball = mgh?

Answer 7

whoops, I mean to say the difference is the energy of the cue ball is that of the 8 ball.

Answer 8

So first figure out the velocity of the 8 ball using energy methods.
Here is the entire system of equations: \[\begin{split}
\frac 12 m(4.2)^2&=\frac 12 m (2.2)^2+\frac 12mv^2\\
vm\cos \theta +2.2m\cos \phi &=4.2m\\
vm\sin \theta +2.2m\sin\phi &=0\\
\end{split}
\]Here is a picture:


As you can see, the vertical components must add up to zero and the horizontal ones should add up to the original momentum.

You have three unknowns: \(v, \theta,\phi\) and three equations.
The constant \(m\) can be divided out from all equations.

Answer 9

@piglet9 My suggestion.

Answer 10

It's great that you are trying to include me in this problem, but its not my question, soI would try to cater your questions to raven.

@wio

Answer 11

Would I have to solve for the other velocity?

Answer 12

I didn't think they would have the same angle

Answer 13

I got a velocity of 3.57771 but I still am unsure how to solve for the angle