Question

If the range and time period of projectile are related to $ R=5{{T}^{2}}, $ then the angle of projection will be

• A. $ \pi /2 $
• B. $ \pi /3 $
• C. $ \pi /4 $
• D. $ \pi /6 $

Answer 1

The Correct Option is C

$ T=\frac{2u\sin \theta }{g} $ $ R=\frac{{{u}^{2}}\sin 2\theta }{g} $ According to question, $ R=5{{T}^{2}} $ $ \frac{{{u}^{2}}\sin 2\theta }{g}=5{{\left( \frac{2u\sin \theta }{g} \right)}^{2}} $ $ \frac{2{{u}^{2}}\sin \theta .\cos \theta }{g}=\frac{20{{u}^{2}}{{\sin }^{2}}\theta }{g} $ $ \cos \theta =\frac{10\sin \theta }{{{g}^{2}}} $ $ \tan \theta =1 $ or $ \theta =\frac{\pi }{4} $