# speed of the ball after collision

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A ball moving with a velocity of 9 meters per second collides with another similar stationary ball. After the collision both the balls move in direction making an angle of 30 degree with the initial direction. After the collision what will the speed of the two balls be?

I used conservation of linear momentum:
$$m9i=2m (\frac {\sqrt3 }{2 }vi+\frac {1}{2}v)j$$
Where $v$ is the final speed and $i$ and $j$ represent unit vectors.

But the answer doesn't come out correctly. What am I doing wrong?

asked Nov 25, 2016
edited Nov 25, 2016
The question is asking for the value of $v$. What answer do you get? What do you think the correct answer is? Your equation cannot be correct because there is no $j$ component on the LHS while the $j$ component on the RHS is non-zero.

The question means that both the balls move at 30 degrees to the original direction, which means the equation would be
$$m9i=2mv\cos\theta i$$
Because the balls have their perpendicular components eliminated in the equation, the answer comes out to be $\frac{9}{\sqrt{3}}$, which comes out to be $5.2$m/sec.

answered Nov 26, 2016 by (2,320 points)
selected Dec 2, 2016