Question

A body is projected at such angle that the horizontal range is three times the greatest height. The angle of projection is

• A. ${42}^o{8}^{\prime }$
• B. ${53}^o{7}^{\prime }$
• C. ${33}^o{7}^{\prime }$
• D. ${25}^o{8}^{\prime }$

Answer 1

Answer: (B)

${53}^o{7}^{\prime }$

$R=3H;R=\frac{u^2\sin 2\theta }{g};H=\frac{u^2{sin}^2\theta }{2g}$

$\frac{u^2\sin 2\theta }{g}=\frac{{3u}^2{sin}^2\theta }{2g}$

$⟹2\sin \theta \cos \theta =\frac{3{sin}^2\theta }{2}$

$\tan \theta =\frac{4}{3}\Rightarrow \theta ={53}^o{7}^{\prime }$