Question

Two balls are projected from the same point in directions inclined at $ {{45}^{o}} $ and $ {{60}^{o}} $ to the horizontal respectively. If they attain the same height, the ratio of their velocities of projection is equal to

• A. $ \sqrt{3}:1 $
• B. $ 3:1 $
• C. $ 3:2 $
• D. $ \sqrt{3}: \sqrt{2} $

Answer 1

Answer: (D)

Let the velocity of two balls at the projection time is
$ {{u}_{1}} $ and $ {{u}_{2}} $
and H be the corresponding height attained by both balls. Height of first ball = Highest of second ball
$ \frac{u_{1}^{2}\,\,{{\sin }^{2}}\,{{45}^{o}}}{2g}=\frac{u_{2}^{2}\,\,{{\sin }^{2}}\,\,{{60}^{o}}}{2g} $
$ \Rightarrow $ $ u_{1}^{2}\times 1/2=u_{2}^{2}\times 3/4 $
$ \Rightarrow $ $ {{u}_{1}}:{{u}_{2}}=\sqrt{3}:\sqrt{2} $