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
$\frac{u_1^2{\sin }^2{45}^o}{2g}=\frac{u_2^2{\sin }^2{60}^o}{2g}$
$\Rightarrow$ $u_1^2\times 1/2=u_2^2\times 3/4$
$\Rightarrow$ $u_1:u_2=\sqrt{3}:\sqrt{2}$