A boy throws a ball with initial speed sqrt(ag) at an angle theta to the horizontal. It strikes a smooth vertical wall and returns to his hand. Show that if the boy is standing at a distance 'a' from the wall, the coefficient of restitution between the ball and the wall equals 1/((4sin2theta-1)).Also show that theta cannot be less than 15^(@).

A boy throws a ball with initial speed sqrt(ag) at an angle theta to t

1.	A boy throws a ball with initial speed sqrt(ag) at an angle theta to the horizontal. It strikes a smooth vertical wall and returns to his hand. Show that if the boy is standing at a distance 'a' from the wall, the coefficient of restitution between the ball and the wall equals 1/((4sin2theta-1)).Also show that theta cannot be less than 15^(@).
Answer» SOLUTION :When the BALL strikes the wall, vertical component `v_(y)` remains UNCHANGED while its horizontal component `ucostheta` becomes `eucostheta` in opposite direction. Now since `v_(y)` remains unchaned during collision, its time of flight `T` will also REMAIN uchanged. Hence `T=t_(OA)+t_(AO)` or `(2usintheta)/g=a/(ucostheta)+a/(eucostheta)` Multiplying the EQUATION by `ucostheta` we get `(2u^(2)sinthetacostheta)/g=a(1+1/e)` or `((5g)(sin2theta))/g=a(1+1/e)` `u=2sqrt(ag)` or `4sin2theta=1+1/e` `e=1/(4sin2theta-1)` Hence 4sintheta-1ge1` or sin2thetage1/2` or `2thetage30^(@)` or `thetage15^(@)`