b
\(v = u\cot \alpha\)

(O)\(\, = \,u \, \sin \alpha\)

Final velocity (at point \(P\)) \(= \,- \,v\cos \alpha \)

\(= - u\cot \alpha \,\cos \alpha\)

Time of flight (from point \(O\) to \(P\)) \(= \,t\)

\(v = u - g\,t\)\( - \,u\cot \alpha \,\cos \alpha \, = \,u\sin \alpha - g\,t\)

\(\therefore \,t = \frac{{u\sin \alpha + u\cot \alpha \,\cos \alpha }}{g}\)

\( = \frac{u}{{g\sin \alpha }}\left[ {{{\sin }^2}\alpha + {{\cos }^2}\alpha } \right]\)

\( = \frac{{u\,\,{\rm{cosec}}\alpha }}{g}\)