Correct Answer - (a) `(u^(2)sin 2 alpha)/(g cos theta)`, (b) `v = (v cos (alpha+theta))/(cos theta)`
(a) `u_(x) = ucos alpha, u_(x) = usin alpha`
`a_(x) = 0 a_(y) = g cos theta`
Time of Flight `T = (2usin alpha)/(g cos theta)`
`R = u cos alpha T`
`R = (u cosalpha.2u sin alpha)/(g cos theta) rArr R = (u^(2)sin 2 alpha)/(g cos theta)`
(b) `vecu_(PB) = vecu_(P) - vecu_(B) rArr vecu_(P) = vecu +vecv_(B)`
For horizontal displacement w.r.t. ground `0`.
`u_(p(x)) = u_(x) +u_(B(x))`
`0 = ucos (theta +alpha) - u_(B) cos theta`
`u_(B) = (ucos (theta +alpha))/(cos theta)`