A particle of mass `m` moving with a speed `u` strikes a smooth horizontal surface at an angle `45^(@)`. The particle rebounds at an angle `phi` with speed `v`. If coefficient of restituion is `(1)/(sqrt(3))`, then angle `phi` is

Answer

2

Explanation

`overset(-)A+overset(-)B=a [(1+cos omegat)hati+sin omega thatj], overset(-)A-overset(-)B=a[(1-cos omega t)hati-sin omegat hatj]`
`|overset(-)A+overset(-)B|=a|2 cos ((omegat)/(2))|, |overset(-)A-overset(-)B|=a |2 sin ((omegat)/(2))|`
`|(overset(-)A+overset(-)B)/(A-B)|=|cot ((omegat)/(2))|=sqrt3 rArr (omegat)/(2)=pi/6 rArr t=2`