1.

A ball is projected from a point in a horizontal plane so as to strike a vertical wall at right angle and afterrebounding from the wall and once from the horizontal plane it returns to the point of projection. Then the co-efficient of restitution (e) for the collisions is : (Assuming it to be same for both the collisions).

Answer»

`1//2`
`1//3`
`1//4`
`1//5`

Solution :`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)`


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