A particle of mass `m` strikes on ground with angle of incidence `45^(@)`. If coefficient of restitution, `e=(1)/(sqrt(2))`, find the velociy after impact and angle of reflection.

Explanation

Refer to figure,
Before collision, `upsilon_(x)=(upsilon)/(sqrt(2)), upsilon_(y)=(upsilon)/(sqrt(2))`
After collision , `upsilon_(x)^(')=(upsilon)/(sqrt(2))(=upsilon_(x))`
As `e=("normal compt. of vel. of separtation")/("normal compt. of vel. of approach")`
`e=(upsilon_(y)^('))/(upsilon_(h))`
`upsilon_(y)^(')=eupsilon_(y)=(1)/(sqrt(2)).(upsilon)/(sqrt(2))=(upsilon)/(2)`
As is clear from figure,
Velocity after impact,
`upsilon^(')=sqrt(upsilon'_(x)^(2) +upsilon'_(y)^(2))=sqrt((upsilon^(2))/(2)+(upsilon^(2))/(4))=(sqrt(3))/(2)upsilon`
If `theta` is angle of reflection,
`tantheta=(upsilon_(x)^('))/(upsilon_(y)^('))=(upsilon)/(sqrt(2)).(2)/(upsilon)=sqrt(2)`
`theta=tan^(-1)sqrt(2)`