1. collision

a smooth sphere P of mass 1 kg moving with speed u collides with a stationary sphere smooth sphere Q also of mass 1kg. the direction of motion of P before the impact makes an angle a with the lines of centers of impact. show the direction of motion of P after the impact makes and angle b with the line of centers of impact where
tan b=2tana/1-e where e is the coefficient of restitution.

the speed in the j direction stays the same before and after so i focus on the i direction of both the spheres before and after.so i get 2 equations.using the PCM formula.
ucosa(1)+1(0)=y+x where y is the the velocity of P after the impact in the i direction and x is the velocity of Q in the i direction after impact. i then use the NELR formula. y-usina/ucosa-0 =-e solving both these i get x=ucosa-usina+eucosa and y=usina-eucosa so tanb=usina/usina-eucosa this does not give me the correct answer. i can explain in further detail the question and my workings in more detail if anyone needs it as i went through it quickly. i can post a diagram aswell if you need it.

2. Re: collision

see diagram for variables used ...

$v+w=u\cos{\alpha}$

$w-v = e \cdot u\cos{\alpha}$

solving system for $w$ and $v$ ...

$w = \dfrac{u\cos{\alpha}(1+e)}{2}$

$v = \dfrac{u\cos{\alpha}(1-e)}{2}$

$\tan{\beta} = \dfrac{u\sin{\alpha}}{v} = \dfrac{u\sin{\alpha}}{1} \cdot \dfrac{2}{u\cos{\alpha}(1-e)} = \dfrac{2\tan{\alpha}}{1-e}$