A ball is projected from a point in a horizontal plane so as to strike a vertical wall at right angle `A`.after rebounding from the wall it strikes the horizontal plane once and returns to the point of projection just before second collision at horizontal surface. Find co-efficient of restitution for the two collisions, assuming it to be same for both the collision.

Options

A. `1//2`
B. `1//3`
C. `1//4`
D. `1//5`

Answer

A

Explanation

`h=(u^(2)sin^(2)theta)/(2g),x=(R)/(2)(u^(2)sinthetacostheta)/(g)`
`V_(1_(x))=eucostheta(larr)`,
`V_(1_(y))=sqrt(2gh)=usin theta(darr)`
`V_(2_(x))=V_(1_(x))=eucostheta(larr)`,
`V_(2_(y))=eu sintheta(uarr)`
From `BtoC`, equation of trajectory gives,
`-h=O-(gx_(1)^(2))/(2(eV)^(2))impliesx_(1)=(eu^(2)sinthetacostheta)/(g)"and"x_(2)=(2V_(2x)V_(2y))/(g)=(2e^(2)u^(2)sin theta cos theta)/(g)`
`because" "x_(1)+x_(2)=x" "implies" "e+2e^(2)=1" "e=(1)/(2)`