question_answer 43)

                  Two particulars are projected in air with speed \[{{\upsilon }_{0}}\] at angle \[{{\theta }_{1}}\] and \[{{\theta }_{2}}\] (both acute) to the horizontal, respectively. If the height reached by the first particle is greater than that of the second, then tick the right choices                 (a) angle of projection : \[{{\theta }_{1}}>{{\theta }_{2}}\]                 (b) time of flight : \[{{T}_{1}}>\,{{T}_{2}}\]                 (c) horizontal range : \[{{R}_{1}}>{{\upsilon }_{2}}\]                 (d) total energy : \[{{U}_{1}}>\text{ }{{U}_{2}}\]

Answer:

                  (a, b) \[H\,=\frac{{{u}^{2}}{{\sin }^{2}}\theta }{2g}\]                                 Since \[{{H}_{1}}>{{H}_{2}}\]                 Also \[T\propto \,\sin \,\theta \,\,\therefore \,\,{{T}_{1}}>\,{{T}_{2}}.\]