A dparticle of mas m moving with speed u collides elastically with a sphere of radius R and same mass at rest, at an impact parameter d. Find
(a) Angle between their final velocities and
(b) Magpitude of their final velocities.

Explanation

As the collision is perfectly elastic and masses of both the particles are same thus their velocity vectors should b e exchanged along the line impact.
Thus `v_(2)=u cos theta and v_(3)=0`
Now id we focus on the particle along there is no force on it parpendicular to the line of impact.
Thus its velocity does not change in this directin and hence.
`v_(1)=usin theta`
Now, from geometry,
`sin theta=(d)/(R)`
`cos theta=sqrt(1-(d^(2))/(R^(2)))`
`impliesv_(2)=u/Rsqrt(R^(2)-d^(2))`
`v_(1)=(ud)/(R)`
`v_(3)=0`