b
(b)

\(\theta=45^{\circ}, t=1 \,s\)

\(\tan \phi=\frac{V_y}{U_y}=\frac{u \sin \theta-g t}{u \cos \theta}\)

\(\tan 45^{\circ}=\frac{u \sin \theta-g \times 1}{u \cos \theta} \Rightarrow u \cos \theta=u \sin \theta-g\)

also, \(V_y=0\), after \(1^{\text {st }}\) (as speed is minimum)

\(u \sin \theta-g \times 2=0\)

\(\Rightarrow u \sin \theta=2 g \ldots (i)\)

so, \(u \cos \theta=2 g-g\)

\(u \cos \theta=g \ldots (ii)\)

so, \(\frac{(i)}{(ii)}=\frac{u \sin \theta}{u \cos \theta}=\frac{2 g}{g}\)

\(\Rightarrow \tan \theta=2\)

\(\theta=\tan ^{-1}(2)\)