this is my first post here :)
Right so this is my question:
Two balls both with mass, xkg each travel on a smooth surface (friction = 0) with different starting velocities. After the particles collide in the collision, they move with different velocities away from each other.
Initial velocity of the first ball/particle = 5^(2/3)
Initial velocity of the second ball/particle = 7^(1/3)
Initially the first ball collides with initial angle 40 degrees to the horizontal and the second ball collides with initial angle 50 degrees to the horizontal.
Finally (after the collision) the particles have different velocities, with ball 1 having velocity z1 and ball 2 having velocity z2, with ball 1 at angle 35 degrees to the horizontal and ball 2 at angle 55 degrees to the horizontal.
I will draw a diagram here, as I think it is difficult to visualize this :)
The questions I have which I want to solve are:
i) Devise equations using linear momentum conservation to find the final velocities of ball 1 and 2.
ii) Show that the initial kinetic energy is the same as the final kinetic energy - if at all.
I will attach my working out here. Although I have some questions.
From past questions, that I have done they never come off at an angle as shown here.
For part i) would I be resolving the initial momentum in the x-direction, and in the y-direction and putting them equal to the respective final directions. As in initial momentum x direction = final momentum x direction. And initial momentum y direction = final momentum y direction.
For part ii) obviously to do this: KE initial = KE final.
But for the velocity of the individual ball, will that be initially: Initial velocity of the first ball/particle = 5^(2/3) Initial velocity of the second ball/particle = 7^(1/3)
And:
Final velocity of the first ball/particle = z1 Final velocity of the second ball/particle = z2
This is what I would think I would do. I will certainly attach my own working out. But if anyone could tell me if I approaching this question right/wrong it would be very helpful.
(If I have made some mistake in posting in the wrong place, or tagged incorrectly or done some other rule violation I am sorry!!!)
Thanks
Alex
UPDATED
Please check/skim/go over these solutions that I have done.
Thank you too david quinn for helping me.
Applying conservation of momentum gives separate component equations as: $$u\cos 40+v\cos 50=z_1\cos 35+z_2\cos 55$$ and $$-u\sin 40+v\sin50=z_1\sin35-z_2\sin 55$$
Where $u=5^{\frac 23}$ and $v=7^{\frac 13}$
Then you can solve simultaneously for $z_1$ and $z_2$