Question

Trajectories of two projectiles are shown in figure. Let $ {{T}_{1}} $ and $ {{T}_{2}} $ be the time periods and $ {{u}_{1}} $ and $ {{u}_{2}} $ their speeds of projection. Then
(1) $ {{T}_{2}}>{{T}_{1}} $ (2) $ {{T}_{1}}={{T}_{2}} $ (3) $ {{u}_{1}}>{{u}_{2}} $ (4) $ {{u}_{1}}<{{u}_{2}} $

• A. 1, 2 and 3 are correct.
• B. 1 and 2 are correct.
• C. 2 and 4 are correct.
• D. 1 and 3 are correct.

Answer 1

Answer: (C)

Maximum height and time of flight depend on the vertical component of initial velocity
$ {{H}_{1}}={{H}_{2}} $
$ \Rightarrow $ $ {{u}_{{{y}_{1}}}}={{u}_{{{y}_{2}}}} $
Here, $ R=\frac{{{u}^{2}}\sin 2\theta }{g}=\frac{2(u\sin \theta )(u\cos \theta )}{g} $
$ =\frac{2{{u}_{x}}{{u}_{y}}}{g} $
$ {{R}_{2}}>{{R}_{1}} $
$ \therefore $ $ {{u}_{{{x}_{2}}}}>{{u}_{{{x}_{1}}}} $ or $ {{u}_{2}}>{{u}_{1}} $