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

Answer: (C)

$\pi /4$

Answer 2

$T=\frac{2u\sin \theta }{g}$ $R=\frac{{{u}^{2}}\sin 2\theta }{g}$ 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 $\theta =\frac{\pi }{4}$