Match the Column I with Column II

Explanation

Applying component of velocities, The x-component of velocity is `u sin theta=vsinphi` ….(1)
The magnitude of y-component of velocity is not same, therefore, using coefficient of restitution
`e=(vcosphi)/(ucosphi)`
Squaring (1) and (2) and adding we get
`v^(2)sin^(2)phi=u^(2)sin^(2)theta`
`v^(2)cos^(2)phi=e^(2)u^(2)cos^(2)theta`
aadding `v^(2)=u^(2)sin^(2)theta+e^(2)u^(2)cos^(2)theta`
`therefore v^(2)=u^(2)[sin^(2)theta+e^(2)cos^(2)theta]`
`therefore v=usqrt(sin^(2)theta+e^(2)cos^(2)theta)`